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pro vyhledávání: '"Davies,James"'
Negami's famous planar cover conjecture is equivalent to the statement that a connected graph can be embedded in the projective plane if and only if it has a projective planar cover. In 1999, Hlin\v{e}n\'y proposed extending this conjecture to higher
Externí odkaz:
http://arxiv.org/abs/2412.04420
Autor:
Campbell, Rutger, Davies, James, Distel, Marc, Frederickson, Bryce, Gollin, J. Pascal, Hendrey, Kevin, Hickingbotham, Robert, Wiederrecht, Sebastian, Wood, David R., Yepremyan, Liana
Treewidth and Hadwiger number are two of the most important parameters in structural graph theory. This paper studies graph classes in which large treewidth implies the existence of a large complete graph minor. To formalise this, we say that a graph
Externí odkaz:
http://arxiv.org/abs/2410.19295
Motivated by colouring minimal Cayley graphs, in 1978, Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by constructing graphs of arbitrarily large girth and chromatic number that have a
Externí odkaz:
http://arxiv.org/abs/2410.05199
Autor:
Davies, James, Yuditsky, Yelena
We prove that for every positive integer $d$ and forest $F$, the class of intersection graphs of axis-aligned boxes in $\mathbb{R}^d$ with no induced $F$ subgraph is (polynomially) $\chi$-bounded.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2407.16882
The stochastic nature of star formation and photon propagation in high-redshift galaxies can result in sizable galaxy-to-galaxy scatter in their properties. Ignoring this scatter by assuming mean quantities can bias estimates of their emissivity and
Externí odkaz:
http://arxiv.org/abs/2406.15237
We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or graph) with no $K$-fat $H$ minor is quasi-isometric to a graph with no $H$ minor. Our counterexample is furthermore not quasi-isometric to a graph with no 2-fat $H$ mi
Externí odkaz:
http://arxiv.org/abs/2405.09383
Autor:
Zhu, Kefan, Sharma, Bibhu, Phan, Phuoc Thien, Davies, James, Thai, Mai Thanh, Hoang, Trung Thien, Nguyen, Chi Cong, Ji, Adrienne, Nicotra, Emanuele, Lovell, Nigel H., Do, Thanh Nho
Work related musculoskeletal disorders (WMSDs) are often caused by repetitive lifting, making them a significant concern in occupational health. Although wearable assist devices have become the norm for mitigating the risk of back pain, most spinal a
Externí odkaz:
http://arxiv.org/abs/2402.02319
Autor:
Bucić, Matija, Davies, James
In 1975 Erd\H{o}s initiated the study of the following very natural question. What can be said about the chromatic number of unit distance graphs in $\mathbb{R}^2$ that have large girth? Over the years this question and its natural extension to $\mat
Externí odkaz:
http://arxiv.org/abs/2312.06898
Publikováno v:
Advances in Combinatorics 2024:5, 16pp
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rz\k{a}\.zewski, Thomass\'e, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains eithe
Externí odkaz:
http://arxiv.org/abs/2311.03341
A class $\mathcal F$ of graphs is $\chi$-bounded if there is a function $f$ such that $\chi(H)\le f(\omega(H))$ for all induced subgraphs $H$ of a graph in $\mathcal F$. If $f$ can be chosen to be a polynomial, we say that $\mathcal F$ is polynomiall
Externí odkaz:
http://arxiv.org/abs/2310.11167