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All Journal Indonesian Journal of Combinatorics
Chula J. Jayawardene
University of Colombo Colombo Sri Lanka
Computer Science & IT Decision Sciences, Operations Research & Management

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Size multipartite Ramsey numbers for small paths versus books Chula J. Jayawardene; Jayampathy Ratnayake
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (209.036 KB) | DOI: 10.19184/ijc.2016.1.1.4

Abstract

Given $j \ge 2$,  for  graphs $G$ and $H$, the size Ramsey multipartite number $m_j(G, H)$ is defined as the smallest natural number $t$ such that any blue red coloring of the edges of the  graph $K_{j \times t}$, necessarily containes a red $G$ or a blue $H$ as subgraphs. Let the book with $n$ pages is defined as the graph $K_1 + K_{1,n}$ and denoted by $B_n$. In this paper, we  obtain the exact values of the size Ramsey numbers $m_j(P_3, H)$ for $j \ge 3$ where  $H$ is a book $B_n$. We also derive some upper and lower bounds for the size Ramsey numbers $m_j(P_4, H)$ where  $H$ is a book $B_n$.
Co-Authors Jayampathy Ratnayake