منابع مشابه
$χ$-bounded Families of Oriented Graphs
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic number of a graph is large enough, either the graph contains a clique of size k or it contains T as an induced subgraph. We discuss some results and open problems about extensions of this conjecture to oriented graphs. We conjecture that for every oriented star S and integer k, if the chromatic numbe...
متن کاملOn (δ, χ)-Bounded Families of Graphs
A family F of graphs is said to be (δ, χ)-bounded if there exists a function f(x) satisfying f(x) → ∞ as x → ∞, such that for any graph G from the family, one has f(δ(G)) ≤ χ(G), where δ(G) and χ(G) denotes the minimum degree and chromatic number of G, respectively. Also for any set {H1,H2, . . . ,Hk} of graphs by Forb(H1,H2, . . . ,Hk) we mean the class of graphs that contain no Hi as an induc...
متن کامل$\chi$-bounded families of oriented graphs
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic number of a graph is large enough, either the graph contains a clique of size k or it contains T as an induced subgraph. We discuss some results and open problems about extensions of this conjecture to oriented graphs. We conjecture that for every oriented star S and integer k, if the chromatic numbe...
متن کاملWorkshop on χ-bounded classes
Schedule Thursday 09:30 Welcome coffee. 10:00 S. Thomassé. Introduction. 10:30 J. Fox. A disproof of Scott’s conjecture. 11:30 Lunch break. 14:00 P. Ossona de Mendez. Low tree-depth decompositions and homomorphism bounds. 15:00 Open problems session. Friday 9:00 P. Seymour. Structure theory for tournaments. 10:00 J. Fox. Graph regularity lemmas. 11:00 A. Scott. T.B.A. 12:00 Lunch break. 14:00 V...
متن کاملPacking bounded-degree spanning graphs from separable families
Let G be a separable family of graphs. Then for all positive constants and ∆ and for every su ciently large integer n, every sequence G1, . . . , Gt ∈ G of graphs of order n and maximum degree at most ∆ such that e(G1)+· · ·+e(Gt) ≤ (1− ) ( n 2 ) packs into Kn. This improves results of Böttcher, Hladký, Piguet, and Taraz when G is the class of trees and of Messuti, Rödl, and Schacht in the case...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2018
ISSN: 0364-9024
DOI: 10.1002/jgt.22252