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pro vyhledávání: '"Janzer, A."'
In 1992, Erd\H{o}s and Hajnal posed the following natural problem: Does there exist, for every $r\in \mathbb{N}$, an integer $F(r)$ such that every graph with chromatic number at least $F(r)$ contains $r$ edge-disjoint cycles on the same vertex set?
Externí odkaz:
http://arxiv.org/abs/2410.02437
Autor:
Janzer, Oliver, Yip, Fredy
A graph $G$ with an even number of edges is called even-decomposable if there is a sequence $V(G)=V_0\supset V_1\supset \dots \supset V_k=\emptyset$ such that for each $i$, $G[V_i]$ has an even number of edges and $V_i\setminus~V_{i+1}$ is an indepen
Externí odkaz:
http://arxiv.org/abs/2409.11152
For two graphs $F,H$ and a positive integer $n$, the function $f_{F,H}(n)$ denotes the largest $m$ such that every $H$-free graph on $n$ vertices contains an $F$-free induced subgraph on $m$ vertices. This function has been extensively studied in the
Externí odkaz:
http://arxiv.org/abs/2409.06650
A zero-one matrix $M$ is said to contain another zero-one matrix $A$ if we can delete some rows and columns of $M$ and replace some $1$-entries with $0$-entries such that the resulting matrix is $A$. The extremal number of $A$, denoted $\operatorname
Externí odkaz:
http://arxiv.org/abs/2403.04728
Given two vertex-ordered graphs $G$ and $H$, the ordered Ramsey number $R_<(G,H)$ is the smallest $N$ such that whenever the edges of a vertex-ordered complete graph $K_N$ are red/blue-coloured, then there is a red (ordered) copy of $G$ or a blue (or
Externí odkaz:
http://arxiv.org/abs/2401.02360
In 1975, Erd\H{o}s asked for the maximum number of edges that an $n$-vertex graph can have if it does not contain two edge-disjoint cycles on the same vertex set. It is known that Tur\'an-type results can be used to prove an upper bound of $n^{3/2+o(
Externí odkaz:
http://arxiv.org/abs/2404.07190
Autor:
Janzer, Barnabás, Montgomery, Richard
The famous tree packing conjecture of Gy\'arf\'as from 1976 says that any sequence of trees $T_1,\ldots,T_n$ such that $|T_i|=i$ for each $i\in [n]$ packs into the complete $n$-vertex graph $K_n$. Packing even just the largest trees in such a sequenc
Externí odkaz:
http://arxiv.org/abs/2403.10515
Autor:
Gemini Team, Anil, Rohan, Borgeaud, Sebastian, Alayrac, Jean-Baptiste, Yu, Jiahui, Soricut, Radu, Schalkwyk, Johan, Dai, Andrew M., Hauth, Anja, Millican, Katie, Silver, David, Johnson, Melvin, Antonoglou, Ioannis, Schrittwieser, Julian, Glaese, Amelia, Chen, Jilin, Pitler, Emily, Lillicrap, Timothy, Lazaridou, Angeliki, Firat, Orhan, Molloy, James, Isard, Michael, Barham, Paul R., Hennigan, Tom, Lee, Benjamin, Viola, Fabio, Reynolds, Malcolm, Xu, Yuanzhong, Doherty, Ryan, Collins, Eli, Meyer, Clemens, Rutherford, Eliza, Moreira, Erica, Ayoub, Kareem, Goel, Megha, Krawczyk, Jack, Du, Cosmo, Chi, Ed, Cheng, Heng-Tze, Ni, Eric, Shah, Purvi, Kane, Patrick, Chan, Betty, Faruqui, Manaal, Severyn, Aliaksei, Lin, Hanzhao, Li, YaGuang, Cheng, Yong, Ittycheriah, Abe, Mahdieh, Mahdis, Chen, Mia, Sun, Pei, Tran, Dustin, Bagri, Sumit, Lakshminarayanan, Balaji, Liu, Jeremiah, Orban, Andras, Güra, Fabian, Zhou, Hao, Song, Xinying, Boffy, Aurelien, Ganapathy, Harish, Zheng, Steven, Choe, HyunJeong, Weisz, Ágoston, Zhu, Tao, Lu, Yifeng, Gopal, Siddharth, Kahn, Jarrod, Kula, Maciej, Pitman, Jeff, Shah, Rushin, Taropa, Emanuel, Merey, Majd Al, Baeuml, Martin, Chen, Zhifeng, Shafey, Laurent El, Zhang, Yujing, Sercinoglu, Olcan, Tucker, George, Piqueras, Enrique, Krikun, Maxim, Barr, Iain, Savinov, Nikolay, Danihelka, Ivo, Roelofs, Becca, White, Anaïs, Andreassen, Anders, von Glehn, Tamara, Yagati, Lakshman, Kazemi, Mehran, Gonzalez, Lucas, Khalman, Misha, Sygnowski, Jakub, Frechette, Alexandre, Smith, Charlotte, Culp, Laura, Proleev, Lev, Luan, Yi, Chen, Xi, Lottes, James, Schucher, Nathan, Lebron, Federico, Rrustemi, Alban, Clay, Natalie, Crone, Phil, Kocisky, Tomas, Zhao, Jeffrey, Perz, Bartek, Yu, Dian, Howard, Heidi, Bloniarz, Adam, Rae, Jack W., Lu, Han, Sifre, Laurent, Maggioni, Marcello, Alcober, Fred, Garrette, Dan, Barnes, Megan, Thakoor, Shantanu, Austin, Jacob, Barth-Maron, Gabriel, Wong, William, Joshi, Rishabh, Chaabouni, Rahma, Fatiha, Deeni, Ahuja, Arun, Tomar, Gaurav Singh, Senter, Evan, Chadwick, Martin, Kornakov, Ilya, Attaluri, Nithya, Iturrate, Iñaki, Liu, Ruibo, Li, Yunxuan, Cogan, Sarah, Chen, Jeremy, Jia, Chao, Gu, Chenjie, Zhang, Qiao, Grimstad, Jordan, Hartman, Ale Jakse, Garcia, Xavier, Pillai, Thanumalayan Sankaranarayana, Devlin, Jacob, Laskin, Michael, Casas, Diego de Las, Valter, Dasha, Tao, Connie, Blanco, Lorenzo, Badia, Adrià Puigdomènech, Reitter, David, Chen, Mianna, Brennan, Jenny, Rivera, Clara, Brin, Sergey, Iqbal, Shariq, Surita, Gabriela, Labanowski, Jane, Rao, Abhi, Winkler, Stephanie, Parisotto, Emilio, Gu, Yiming, Olszewska, Kate, Addanki, Ravi, Miech, Antoine, Louis, Annie, Teplyashin, Denis, Brown, Geoff, Catt, Elliot, Balaguer, Jan, Xiang, Jackie, Wang, Pidong, Ashwood, Zoe, Briukhov, Anton, Webson, Albert, Ganapathy, Sanjay, Sanghavi, Smit, Kannan, Ajay, Chang, Ming-Wei, Stjerngren, Axel, Djolonga, Josip, Sun, Yuting, Bapna, Ankur, Aitchison, Matthew, Pejman, Pedram, Michalewski, Henryk, Yu, Tianhe, Wang, Cindy, Love, Juliette, Ahn, Junwhan, Bloxwich, Dawn, Han, Kehang, Humphreys, Peter, Sellam, Thibault, Bradbury, James, Godbole, Varun, Samangooei, Sina, Damoc, Bogdan, Kaskasoli, Alex, Arnold, Sébastien M. R., Vasudevan, Vijay, Agrawal, Shubham, Riesa, Jason, Lepikhin, Dmitry, Tanburn, Richard, Srinivasan, Srivatsan, Lim, Hyeontaek, Hodkinson, Sarah, Shyam, Pranav, Ferret, Johan, Hand, Steven, Garg, Ankush, Paine, Tom Le, Li, Jian, Li, Yujia, Giang, Minh, Neitz, Alexander, Abbas, Zaheer, York, Sarah, Reid, Machel, Cole, Elizabeth, Chowdhery, Aakanksha, Das, Dipanjan, Rogozińska, Dominika, Nikolaev, Vitaliy, Sprechmann, Pablo, Nado, Zachary, Zilka, Lukas, Prost, Flavien, He, Luheng, Monteiro, Marianne, Mishra, Gaurav, Welty, Chris, Newlan, Josh, Jia, Dawei, Allamanis, Miltiadis, Hu, Clara Huiyi, de Liedekerke, Raoul, Gilmer, Justin, Saroufim, Carl, Rijhwani, Shruti, Hou, Shaobo, Shrivastava, Disha, Baddepudi, Anirudh, Goldin, Alex, Ozturel, Adnan, Cassirer, Albin, Xu, Yunhan, Sohn, Daniel, Sachan, Devendra, Amplayo, Reinald Kim, Swanson, Craig, Petrova, Dessie, Narayan, Shashi, Guez, Arthur, Brahma, Siddhartha, Landon, Jessica, Patel, Miteyan, Zhao, Ruizhe, Villela, Kevin, Wang, Luyu, Jia, Wenhao, Rahtz, Matthew, Giménez, Mai, Yeung, Legg, Keeling, James, Georgiev, Petko, Mincu, Diana, Wu, Boxi, Haykal, Salem, Saputro, Rachel, Vodrahalli, Kiran, Qin, James, Cankara, Zeynep, Sharma, Abhanshu, Fernando, Nick, Hawkins, Will, Neyshabur, Behnam, Kim, Solomon, Hutter, Adrian, Agrawal, Priyanka, Castro-Ros, Alex, Driessche, George van den, Wang, Tao, Yang, Fan, Chang, Shuo-yiin, Komarek, Paul, McIlroy, Ross, Lučić, Mario, Zhang, Guodong, Farhan, Wael, Sharman, Michael, Natsev, Paul, Michel, Paul, Bansal, Yamini, Qiao, Siyuan, Cao, Kris, Shakeri, Siamak, Butterfield, Christina, Chung, Justin, Rubenstein, Paul Kishan, Agrawal, Shivani, Mensch, Arthur, Soparkar, Kedar, Lenc, Karel, Chung, Timothy, Pope, Aedan, Maggiore, Loren, Kay, Jackie, Jhakra, Priya, Wang, Shibo, Maynez, Joshua, Phuong, Mary, Tobin, Taylor, Tacchetti, Andrea, Trebacz, Maja, Robinson, Kevin, Katariya, Yash, Riedel, Sebastian, Bailey, Paige, Xiao, Kefan, Ghelani, Nimesh, Aroyo, Lora, Slone, Ambrose, 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Justin, Lorenzo, Jaime Alonso, Sjösund, Lars Lowe, Cevey, Sébastien, Gleicher, Zach, Avrahami, Thi, Boral, Anudhyan, Srinivasan, Hansa, Selo, Vittorio, May, Rhys, Aisopos, Konstantinos, Hussenot, Léonard, Soares, Livio Baldini, Baumli, Kate, Chang, Michael B., Recasens, Adrià, Caine, Ben, Pritzel, Alexander, Pavetic, Filip, Pardo, Fabio, Gergely, Anita, Frye, Justin, Ramasesh, Vinay, Horgan, Dan, Badola, Kartikeya, Kassner, Nora, Roy, Subhrajit, Dyer, Ethan, Campos, Víctor Campos, Tomala, Alex, Tang, Yunhao, Badawy, Dalia El, White, Elspeth, Mustafa, Basil, Lang, Oran, Jindal, Abhishek, Vikram, Sharad, Gong, Zhitao, Caelles, Sergi, Hemsley, Ross, Thornton, Gregory, Feng, Fangxiaoyu, Stokowiec, Wojciech, Zheng, Ce, Thacker, Phoebe, Ünlü, Çağlar, Zhang, Zhishuai, Saleh, Mohammad, Svensson, James, Bileschi, Max, Patil, Piyush, Anand, Ankesh, Ring, Roman, Tsihlas, Katerina, Vezer, Arpi, Selvi, Marco, Shevlane, Toby, Rodriguez, Mikel, Kwiatkowski, Tom, Daruki, Samira, Rong, Keran, Dafoe, Allan, FitzGerald, Nicholas, Gu-Lemberg, Keren, Khan, Mina, Hendricks, Lisa Anne, Pellat, Marie, Feinberg, Vladimir, Cobon-Kerr, James, Sainath, Tara, Rauh, Maribeth, Hashemi, Sayed Hadi, Ives, Richard, Hasson, Yana, Noland, Eric, Cao, Yuan, Byrd, Nathan, Hou, Le, Wang, Qingze, Sottiaux, Thibault, Paganini, Michela, Lespiau, Jean-Baptiste, Moufarek, Alexandre, Hassan, Samer, Shivakumar, Kaushik, van Amersfoort, Joost, Mandhane, Amol, Joshi, Pratik, Goyal, Anirudh, Tung, Matthew, Brock, Andrew, Sheahan, Hannah, Misra, Vedant, Li, Cheng, Rakićević, Nemanja, Dehghani, Mostafa, Liu, Fangyu, Mittal, Sid, Oh, Junhyuk, Noury, Seb, Sezener, Eren, Huot, Fantine, Lamm, Matthew, De Cao, Nicola, Chen, Charlie, Mudgal, Sidharth, Stella, Romina, Brooks, Kevin, Vasudevan, Gautam, Liu, Chenxi, Chain, Mainak, Melinkeri, Nivedita, Cohen, Aaron, Wang, Venus, Seymore, Kristie, Zubkov, Sergey, Goel, Rahul, Yue, Summer, Krishnakumaran, Sai, Albert, Brian, Hurley, Nate, Sano, Motoki, Mohananey, Anhad, 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Shivanna, Rakesh, Chuklin, Aleksandr, Li, Josie, Spadine, Carrie, Wolfe, Travis, Mohamed, Kareem, Das, Subhabrata, Dai, Zihang, He, Kyle, von Dincklage, Daniel, Upadhyay, Shyam, Maurya, Akanksha, Chi, Luyan, Krause, Sebastian, Salama, Khalid, Rabinovitch, Pam G, M, Pavan Kumar Reddy, Selvan, Aarush, Dektiarev, Mikhail, Ghiasi, Golnaz, Guven, Erdem, Gupta, Himanshu, Liu, Boyi, Sharma, Deepak, Shtacher, Idan Heimlich, Paul, Shachi, Akerlund, Oscar, Aubet, François-Xavier, Huang, Terry, Zhu, Chen, Zhu, Eric, Teixeira, Elico, Fritze, Matthew, Bertolini, Francesco, Marinescu, Liana-Eleonora, Bölle, Martin, Paulus, Dominik, Gupta, Khyatti, Latkar, Tejasi, Chang, Max, Sanders, Jason, Wilson, Roopa, Wu, Xuewei, Tan, Yi-Xuan, Thiet, Lam Nguyen, Doshi, Tulsee, Lall, Sid, Mishra, Swaroop, Chen, Wanming, Luong, Thang, Benjamin, Seth, Lee, Jasmine, Andrejczuk, Ewa, Rabiej, Dominik, Ranjan, Vipul, Styrc, Krzysztof, Yin, Pengcheng, Simon, Jon, Harriott, Malcolm Rose, Bansal, Mudit, Robsky, Alexei, Bacon, Geoff, Greene, David, Mirylenka, Daniil, Zhou, Chen, Sarvana, Obaid, Goyal, Abhimanyu, Andermatt, Samuel, Siegler, Patrick, Horn, Ben, Israel, Assaf, Pongetti, Francesco, Chen, Chih-Wei "Louis", Selvatici, Marco, Silva, Pedro, Wang, Kathie, Tolins, Jackson, Guu, Kelvin, Yogev, Roey, Cai, Xiaochen, Agostini, Alessandro, Shah, Maulik, Nguyen, Hung, Donnaile, Noah Ó, Pereira, Sébastien, Friso, Linda, Stambler, Adam, Kuang, Chenkai, Romanikhin, Yan, Geller, Mark, Yan, ZJ, Jang, Kane, Lee, Cheng-Chun, Fica, Wojciech, Malmi, Eric, Tan, Qijun, Banica, Dan, Balle, Daniel, Pham, Ryan, Huang, Yanping, Avram, Diana, Shi, Hongzhi, Singh, Jasjot, Hidey, Chris, Ahuja, Niharika, Saxena, Pranab, Dooley, Dan, Potharaju, Srividya Pranavi, O'Neill, Eileen, Gokulchandran, Anand, Foley, Ryan, Zhao, Kai, Dusenberry, Mike, Liu, Yuan, Mehta, Pulkit, Kotikalapudi, Ragha, Safranek-Shrader, Chalence, Goodman, Andrew, Kessinger, Joshua, Globen, Eran, Kolhar, Prateek, Gorgolewski, Chris, Ibrahim, Ali, Song, Yang, Eichenbaum, Ali, Brovelli, Thomas, Potluri, Sahitya, Lahoti, Preethi, Baetu, Cip, Ghorbani, Ali, Chen, Charles, Crawford, Andy, Pal, Shalini, Sridhar, Mukund, Gurita, Petru, Mujika, Asier, Petrovski, Igor, Cedoz, Pierre-Louis, Li, Chenmei, Chen, Shiyuan, Santo, Niccolò Dal, Goyal, Siddharth, Punjabi, Jitesh, Kappaganthu, Karthik, Kwak, Chester, LV, Pallavi, Velury, Sarmishta, Choudhury, Himadri, Hall, Jamie, Shah, Premal, Figueira, Ricardo, Thomas, Matt, Lu, Minjie, Zhou, Ting, Kumar, Chintu, Jurdi, Thomas, Chikkerur, Sharat, Ma, Yenai, Yu, Adams, Kwak, Soo, Ähdel, Victor, Rajayogam, Sujeevan, Choma, Travis, Liu, Fei, Barua, Aditya, Ji, Colin, Park, Ji Ho, Hellendoorn, Vincent, Bailey, Alex, Bilal, Taylan, Zhou, Huanjie, Khatir, Mehrdad, Sutton, Charles, Rzadkowski, Wojciech, Macintosh, Fiona, Shagin, Konstantin, Medina, Paul, Liang, Chen, Zhou, Jinjing, Shah, Pararth, Bi, Yingying, Dankovics, Attila, Banga, Shipra, Lehmann, Sabine, Bredesen, Marissa, Lin, Zifan, Hoffmann, John Eric, Lai, Jonathan, Chung, Raynald, Yang, Kai, Balani, Nihal, Bražinskas, Arthur, Sozanschi, Andrei, Hayes, Matthew, Alcalde, Héctor Fernández, Makarov, Peter, Chen, Will, Stella, Antonio, Snijders, Liselotte, Mandl, Michael, Kärrman, Ante, Nowak, Paweł, Wu, Xinyi, Dyck, Alex, Vaidyanathan, Krishnan, R, Raghavender, Mallet, Jessica, Rudominer, Mitch, Johnston, Eric, Mittal, Sushil, Udathu, Akhil, Christensen, Janara, Verma, Vishal, Irving, Zach, Santucci, Andreas, Elsayed, Gamaleldin, Davoodi, Elnaz, Georgiev, Marin, Tenney, Ian, Hua, Nan, Cideron, Geoffrey, Leurent, Edouard, Alnahlawi, Mahmoud, Georgescu, Ionut, Wei, Nan, Zheng, Ivy, Scandinaro, Dylan, Jiang, Heinrich, Snoek, Jasper, Sundararajan, Mukund, Wang, Xuezhi, Ontiveros, Zack, Karo, Itay, Cole, Jeremy, Rajashekhar, Vinu, Tumeh, Lara, Ben-David, Eyal, Jain, Rishub, Uesato, Jonathan, Datta, Romina, Bunyan, Oskar, Wu, Shimu, Zhang, John, Stanczyk, Piotr, Zhang, Ye, Steiner, David, Naskar, Subhajit, Azzam, Michael, Johnson, Matthew, Paszke, Adam, Chiu, Chung-Cheng, Elias, Jaume Sanchez, Mohiuddin, Afroz, Muhammad, Faizan, Miao, Jin, Lee, Andrew, Vieillard, Nino, Park, Jane, Zhang, Jiageng, Stanway, Jeff, Garmon, Drew, Karmarkar, Abhijit, Dong, Zhe, Lee, Jong, Kumar, Aviral, Zhou, Luowei, Evens, Jonathan, Isaac, William, Irving, Geoffrey, Loper, Edward, Fink, Michael, Arkatkar, Isha, Chen, Nanxin, Shafran, Izhak, Petrychenko, Ivan, Chen, Zhe, Jia, Johnson, Levskaya, Anselm, Zhu, Zhenkai, Grabowski, Peter, Mao, Yu, Magni, Alberto, Yao, Kaisheng, Snaider, Javier, Casagrande, Norman, Palmer, Evan, Suganthan, Paul, Castaño, Alfonso, Giannoumis, Irene, Kim, Wooyeol, Rybiński, Mikołaj, Sreevatsa, Ashwin, Prendki, Jennifer, Soergel, David, Goedeckemeyer, Adrian, Gierke, Willi, Jafari, Mohsen, Gaba, Meenu, Wiesner, Jeremy, Wright, Diana Gage, Wei, Yawen, Vashisht, Harsha, Kulizhskaya, Yana, Hoover, Jay, Le, Maigo, Li, Lu, Iwuanyanwu, Chimezie, Liu, Lu, Ramirez, Kevin, Khorlin, Andrey, Cui, Albert, LIN, Tian, Wu, 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Carpenter, John, Papamakarios, George, Kemp, Rupert, Kafle, Sushant, Grunina, Tanya, Sinha, Rishika, Talbert, Alice, Wu, Diane, Owusu-Afriyie, Denese, Thornton, Chloe, Pont-Tuset, Jordi, Narayana, Pradyumna, Li, Jing, Fatehi, Saaber, Wieting, John, Ajmeri, Omar, Uria, Benigno, Ko, Yeongil, Knight, Laura, Héliou, Amélie, Niu, Ning, Gu, Shane, Pang, Chenxi, Li, Yeqing, Levine, Nir, Stolovich, Ariel, Santamaria-Fernandez, Rebeca, Goenka, Sonam, Yustalim, Wenny, Strudel, Robin, Elqursh, Ali, Deck, Charlie, Lee, Hyo, Li, Zonglin, Levin, Kyle, Hoffmann, Raphael, Holtmann-Rice, Dan, Bachem, Olivier, Arora, Sho, Koh, Christy, Yeganeh, Soheil Hassas, Põder, Siim, Tariq, Mukarram, Sun, Yanhua, Ionita, Lucian, Seyedhosseini, Mojtaba, Tafti, Pouya, Liu, Zhiyu, Gulati, Anmol, Liu, Jasmine, Ye, Xinyu, Chrzaszcz, Bart, Wang, Lily, Sethi, Nikhil, Li, Tianrun, Brown, Ben, Singh, Shreya, Fan, Wei, Parisi, Aaron, Stanton, Joe, Koverkathu, Vinod, Choquette-Choo, Christopher A., Li, Yunjie, Lu, TJ, Shroff, 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Amar, Hsiao, Sissie, Hassabis, Demis, Kavukcuoglu, Koray, Sadovsky, Adam, Le, Quoc, Strohman, Trevor, Wu, Yonghui, Petrov, Slav, Dean, Jeffrey, Vinyals, Oriol
This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging fro
Externí odkaz:
http://arxiv.org/abs/2312.11805
Let $f(n, v, e)$ denote the maximum number of edges in a 3-uniform hypergraph on $n$ vertices which does not contain $v$ vertices spanning at least $e$ edges. A central problem in extremal combinatorics, famously posed by Brown, Erd\H{o}s and S\'os i
Externí odkaz:
http://arxiv.org/abs/2311.12765
Autor:
Baber, Rahil, Behague, Natalie, Calbet, Asier, Ellis, David, Erde, Joshua, Gray, Ron, Ivan, Maria-Romina, Janzer, Barnabás, Johnson, Robert, Milićević, Luka, Talbot, John, Tan, Ta Sheng, Wickes, Belinda
One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems in combinatorics has been put together by a subset of his former PhD s
Externí odkaz:
http://arxiv.org/abs/2310.18163