For most graphs H , most H -free graphs have a linear homogeneous set
نویسندگان
چکیده
منابع مشابه
For most graphs H, most H-free graphs have a linear homogeneous set
Erdős and Hajnal conjectured that for every graph H there is a constant ε = ε(H) > 0 such that every graph G that does not have H as an induced subgraph contains a clique or a stable set of order Ω(|V (G)|ε). The conjecture would be false if we set ε = 1; however, in an asymptotic setting, we obtain this strengthened form of Erdős and Hajnal’s conjecture for almost every graph H, and in particu...
متن کاملAlmost all H-free graphs have the Erdős-Hajnal property
Erdős and Hajnal conjectured that, for every graph H, there exists a constant (H) > 0 such that every H-free graph G (that is, not containing H as an induced subgraph) must contain a clique or an independent set of size at least |G| . We prove that there exists (H) such that almost every H-free graph G has this property, meaning that, amongst the H-free graphs with n vertices, the proportion ha...
متن کاملLinear kernels for (connected) dominating set on H-minor-free graphs
We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a minor. In other words, we give polynomial time algorithms that, for a given H-minor free graph G and positive integer k, output an H-minor free graph G′ on O(k) vertices such that G has a (connected) dominating set of size k if and only if G′ has. Prior to our work,...
متن کاملChoosability on H-free graphs
A graph is H-free if it has no induced subgraph isomorphic to H. We determine the computational complexity of the Choosability problem restricted to H-free graphs for every graph H that does not belong to {K1,3, P1 +P2, P1 +P3, P4}. We also show that if H is a linear forest, then the problem is fixed-parameter tractable when parameterized by k.
متن کاملMaxCut in H-free graphs
For a graph G, let f(G) denote the maximum number of edges in a cut of G. For an integer m and for a fixed graph H, let f(m,H) denote the minimum possible cardinality of f(G), as G ranges over all graphs on m edges that contain no copy of H. In this paper we study this function for various graphs H. In particular we show that for any graph H obtained by connecting a single vertex to all vertice...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2013
ISSN: 1042-9832
DOI: 10.1002/rsa.20488