Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Lee, Joonkyung"'
A graph $H$ is said to be positive if the homomorphism density $t_H(G)$ is non-negative for all weighted graphs $G$. The positive graph conjecture proposes a characterisation of such graphs, saying that a graph is positive if and only if it is symmet
Externí odkaz:
http://arxiv.org/abs/2404.17467
Autor:
Mehrabian, Abbas, Anand, Ankit, Kim, Hyunjik, Sonnerat, Nicolas, Balog, Matej, Comanici, Gheorghe, Berariu, Tudor, Lee, Andrew, Ruoss, Anian, Bulanova, Anna, Toyama, Daniel, Blackwell, Sam, Paredes, Bernardino Romera, Veličković, Petar, Orseau, Laurent, Lee, Joonkyung, Naredla, Anurag Murty, Precup, Doina, Wagner, Adam Zsolt
This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this pro
Externí odkaz:
http://arxiv.org/abs/2311.03583
Sidorenko's conjecture states that, for all bipartite graphs $H$, quasirandom graphs contain asymptotically the minimum number of copies of $H$ taken over all graphs with the same order and edge density. While still open for graphs, the analogous sta
Externí odkaz:
http://arxiv.org/abs/2307.04588
Autor:
Conlon, David, Lee, Joonkyung
We say that a graph $H$ dominates another graph $H'$ if the number of homomorphisms from $H'$ to any graph $G$ is dominated, in an appropriate sense, by the number of homomorphisms from $H$ to $G$. We study the family of dominating graphs, those grap
Externí odkaz:
http://arxiv.org/abs/2303.01997
We prove that every properly edge-colored $n$-vertex graph with average degree at least $100(\log n)^2$ contains a rainbow cycle, improving upon $(\log n)^{2+o(1)}$ bound due to Tomon. We also prove that every properly colored $n$-vertex graph with a
Externí odkaz:
http://arxiv.org/abs/2211.03291
Autor:
Kim, Jang Soo, Lee, Joonkyung
A graph $H$ is \emph{common} if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is asymptotically minimised by the random colouring, or equivalently, $t_H(W)+t_H(1-W)\geq 2^{1-e(H)}$ holds for every graphon
Externí odkaz:
http://arxiv.org/abs/2210.00977
We prove that the family of graphs containing no cycle with exactly $k$-chords is $\chi$-bounded, for $k$ large enough or of form $\ell(\ell-2)$ with $\ell \ge 3$ an integer. This verifies (up to a finite number of values $k$) a conjecture of Aboulke
Externí odkaz:
http://arxiv.org/abs/2208.14860
Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and R\"{o}dl conjectured that for any given $\mu>0$, there exists $n_0$ such that the following holds. Every $n$-vertex Steiner triple system contains
Externí odkaz:
http://arxiv.org/abs/2208.10370
Autor:
Ko, Sejin, Lee, Joonkyung
A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is asymptotically minimised by the random colouring. We prove that, given $k,r>0$, there exists a $k$-connected common graph with chr
Externí odkaz:
http://arxiv.org/abs/2207.09427
Autor:
Kim, Jang Soo, Lee, Joonkyung
Publikováno v:
In Journal of Combinatorial Theory, Series B May 2024 166:109-122
