The potential-Ramsey numbers rpot(Cn,Kt−k) and rpot(Pn,Kt−k)

Liang Zhang and Jianhua Yin

Applied Mathematics and Computation, 2023, vol. 451, issue C

Abstract: A nonincreasing sequence ρ=(ρ1,…,ρn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. In this case, G is referred to as a realization of ρ. Given two graphs G1 and G2, Busch et al. introduced the potential-Ramsey number of G1 and G2, denoted rpot(G1,G2), is the smallest nonnegative integer m such that for every m-term graphic sequence ρ, there is a realization G of ρ with G1⊆G or with G2⊆G¯, where G¯ is the complement of G. For t≥2 and 0≤k≤⌊t2⌋, let Kt−k be the graph obtained from Kt by deleting k independent edges. Busch et al. determined rpot(Cn,Kt−k) and rpot(Pn,Kt−k) for k=0. Du and Yin determined rpot(Cn,Kt−k) and rpot(Pn,Kt−k) for k=1. In this paper, we further determine rpot(Cn,Kt−k) and rpot(Pn,Kt−k) for 2≤k≤⌊t2⌋.

Keywords: Degree sequence; Potential-Ramsey number (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323002047

DOI: 10.1016/j.amc.2023.128035

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