Zobrazeno 1 - 10
of 22
pro vyhledávání: '"05C15, 05D10"'
Autor:
Reiher, Christian
This survey on graphs of large girth consists of two parts. The first deals with some aspects of algebraic and extremal graph theory loosely related to the Moore bound. Our point of departure for the second, Ramsey theoretic, part are some constructi
Externí odkaz:
http://arxiv.org/abs/2403.13571
Autor:
Reiher, Christian
Erd\H{o}s and Hajnal proved that every graph of uncountable chromatic number contains arbitrarily large finite, complete, bipartite graphs. We extend this result to hypergraphs.
Comment: 2 figures
Comment: 2 figures
Externí odkaz:
http://arxiv.org/abs/2403.11223
Autor:
Bowler, Nathan, Gut, Florian
We investigate a two player game called the $K^4$-building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on some vertex set of size four for themself. The first player to accompli
Externí odkaz:
http://arxiv.org/abs/2309.02132
Publikováno v:
Discrete & Computational Geometry (2024)
We prove that for any $\ell_p$-norm in the plane with $1
Externí odkaz:
http://arxiv.org/abs/2308.08840
We determine the exact value of the $2$-color Ramsey number of a connected $4$-clique matching $\mathscr{C}(nK_4)$ which is a set of connected graphs containing $n$ disjoint $K_4$. That is, we show that $R_2(\mathscr{C}(nK_4)) = 13n-3$ for any positi
Externí odkaz:
http://arxiv.org/abs/2306.08412
We investigate Maker-Breaker games on graphs of size $\aleph_1$ in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove that there is
Externí odkaz:
http://arxiv.org/abs/2201.08681
Autor:
Dobrinen, Natasha, Wang, Kaiyun
We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures,extending Zheng's work for the profinite graph to the setting of Fra\"{\i}ss\'{e} classes of finite ordered binary relational structures wit
Externí odkaz:
http://arxiv.org/abs/2012.08736
Autor:
Zhao, Qinghong, Wei, Bing
Given a graph $H$ and an integer $k\ge1$, the Gallai-Ramsey number $GR_k(H)$ is defined to be the minimum integer $n$ such that every $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $H$
Externí odkaz:
http://arxiv.org/abs/2008.00361
We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs. In both our results, we permit the amount of colour made available to
Externí odkaz:
http://arxiv.org/abs/1812.01534
The Ramsey multiplicity constant of a graph $H$ is the minimum proportion of copies of $H$ in the complete graph which are monochromatic under an edge-coloring of $K_n$ as $n$ goes to infinity. Graphs for which this minimum is asymptotically achieved
Externí odkaz:
http://arxiv.org/abs/1801.00474