On the Restricted Size Ramsey Number Involving a Path P3

Autor: Edy Tri Baskoro, Saladin Uttunggadewa, Denny Riama Silaban
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Discussiones Mathematicae Graph Theory, Vol 39, Iss 3, Pp 757-769 (2019)
ISSN: 2083-5892
Popis: For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey number r*(G,H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G,H), and bounded below by e(G) + e(H) − 1. Moreover, trivially, ̂r(G,H) ≤ r*(G,H). When introducing the size Ramsey number for graph, Erdős et al. (1978) asked two questions; (1) Do there exist graphs G and H such that ˆr(G,H) attains the upper bound? and (2) Do there exist graphs G and H such that ̂r(G,H) is significantly less than the upper bound?
Databáze: OpenAIRE