Erdős--Lovász Tihany猜想综述

A Survey on the Erdős--Lovász Tihany Conjecture

设s≥2和t≥2是整数.若可将V(G)分割成两个集合S和T,使得χ(G[S])≥s且χ(G[T])≥t,则称图G为(s,t)-可分裂的.1968年提出的著名猜想——Erdős--Lovász Tihany猜想称,所有满足ω(G)<χ(G)=s+t−1的图G都是(s,t)-可分裂的.本文是关于Erdős--Lovász Tihany猜想及相关问题的一个综述.

Let s≥2 and t≥2 be integers.A graph G is(s,t)-splittable if V(G)can be partitioned into two sets S and T such thatχ(G[S])≥s andχ(G[T])≥t.The famous Erd̋os–Lov́asz Tihany Conjecture established in 1968 states that every graph G withω(G)<χ(G)=s+t−1 is(s,t)-splittable.We provide a survey on the Erdos–Lovasz Tihany Conjecture and its related problems.