Abstract
For given simple graphs H1,H2,…,Hc,the multicolor Ramsey number R(H1,H2,...,Hc)is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1 of the complete graph Kn,at least one Gi has a subgraph isomorphic to Hi.Let m,n1,n2,...,nc be positive integers and Σ=Σci=1(ni-1).Some bounds and exact values of R(K1,n1,...,K1,nc,Pm)have been obtained in literature.Wang(Graphs Combin.,2020)conjec-tured that if Σ(≠)0(mod m-1)and Σ+1 ≥(m-3)2,then R(K1,n1,...,K1,nc,Pm)=Σ+m-1.In this note,we give a new lower bound and some exact values of R(K1,n1,...,K1,nc,Pm)pro-vided m ≤ Σ,Σ ≡ k(mod m-1),and 2 ≤ k ≤ m-2.These results partially confirm Wang's conjecture.
基金项目
National Natural Science Foundation of China(12071453)
National Key R and D Program of China(2020YFA0713100)
Innovation Program for Quantum Science and Technology(2021ZD0302902)
NETL
NSTL
万方数据