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A coloring of the edges of a graph $G$ in which every $K_{1,2}$ is totally multicolored is known as a proper coloring and a coloring of the edges of $G$ in which every $K_{1,2}$ and every $K_{2,2}$ is totally multicolored is called a B-coloring. In t
Externí odkaz:
http://arxiv.org/abs/2408.09081
We call a proper edge coloring of a graph $G$ a B-coloring if every 4-cycle of $G$ is colored with four different colors. Let $q_B(G)$ denote the smallest number of colors needed for a B-coloring of $G$. Motivated by earlier papers on B-colorings, he
Externí odkaz:
http://arxiv.org/abs/2408.09059
Assume that $R_1,R_2,\dots,R_t$ are disjoint parallel lines in the plane. A $t$-interval (or $t$-track interval) is a set that can be written as the union of $t$ closed intervals, each on a different line. It is known that pairwise intersecting $2$-i
Externí odkaz:
http://arxiv.org/abs/2408.04308
Autor:
Gyarfas, Andras, Sarkozy, Gabor N.
In this paper we study Tur\'an and Ramsey numbers in linear triple systems, defined as $3$-uniform hypergraphs in which any two triples intersect in at most one vertex. A famous result of Ruzsa and Szemer\'edi is that for any fixed $c>0$ and large en
Externí odkaz:
http://arxiv.org/abs/2011.13678
A path-matching of order $p$ is a vertex disjoint union of nontrivial paths spanning $p$ vertices. Burr and Roberts, and Faudree and Schelp determined the 2-color Ramsey number of path-matchings. In this paper we study the multicolor Ramsey number of
Externí odkaz:
http://arxiv.org/abs/1909.01920
Akademický článek
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It is well-known that in every $r$-coloring of the edges of the complete bipartite graph $K_{m,n}$ there is a monochromatic connected component with at least ${m+n\over r}$ vertices. In this paper we study an extension of this problem by replacing co
Externí odkaz:
http://arxiv.org/abs/1806.05271
It is well-known that in every $r$-coloring of the edges of the complete bipartite graph $K_{n,n}$ there is a monochromatic connected component with at least ${2n\over r}$ vertices. It would be interesting to know whether we can additionally require
Externí odkaz:
http://arxiv.org/abs/1804.04195
Autor:
Gyárfás, András, Sárközy, Gábor N.
Publikováno v:
In Discrete Mathematics November 2022 345(11)
