On the restricted size Ramsey number for P3 versus dense connected graphs

Electronic Journal of Graph Theory and Applications

Saladin Uttunggadewa¹  Edy Tri Baskoro¹  Denny Riama Silaban² 

[1] Combinatorial Mathematics Research GroupFaculty of Mathematics and Natural SciencesInstitut Teknologi Bandung;Department of Mathematics, Faculty of Mathematics and Natural Sciences, UniversitasIndonesia;

关键词: restricted size ramsey number, size ramsey number, dense connected graph, path;   

DOI  :  10.5614/ejgta.2020.8.2.14

来源: DOAJ

【 摘 要 】

Let F, G and H be simple graphs. A graph F is said a (G,H)-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H. The size Ramsey number of G and H, ŕ(G,H), is the minimum size of F. If the order of F equals to the Ramsey number of G and H, r(G,H), then the minimum size of F is called the restricted size Ramsey number of G and H, r^*(G,H). The Ramsey number of G and H, r(G,H), is the minimum order of F. In this paper, we study the restricted size number involving a P₃.  The value of r^*(P₃,K_n) has been given by Faudree and Sheehan. Here, we examine r^*(P₃,H) where H is dense connected graph.

【 授权许可】

Unknown