Article Per Year (5 Year)
p-Index From 2019 - 2024
0
P-Index
This Author published in this journals
All Journal Indonesian Journal of Combinatorics
Lilanthi Samarasekara
University of Colombo
Computer Science & IT Decision Sciences, Operations Research & Management

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
A strict upper bound for size multipartite Ramsey numbers of paths versus stars Chula Jayawardene; Lilanthi Samarasekara
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (188.112 KB) | DOI: 10.19184/ijc.2017.1.2.2

Abstract

Let $P_n$ represent the path of size $n$. Let $K_{1,m-1}$ represent a star of size $m$ and be denoted by $S_{m}$. Given a two coloring of the edges of a complete graph $K_{j \times s}$ we say that $K_{j \times s}\rightarrow (P_n,S_{m+1})$ if there is a copy of $P_n$ in the first color or a copy of $S_{m+1}$ in the second color. The size Ramsey multipartite number $m_j(P_n, S_{m+1})$ is the smallest natural number $s$ such that $K_{j \times s}\rightarrow (P_n,S_{m+1})$. Given $j,n,m$ if $s=\left\lceil \dfrac{n+m-1-k}{j-1} \right\rceil$, in this paper, we show that the size Ramsey numbers $m_j(P_n,S_{m+1})$ is bounded above by $s$ for $k=\left\lceil \dfrac{n-1}{j} \right\rceil$. Given $j\ge 3$ and $s$, we will obtain an infinite class $(n,m)$ that achieves this upper bound $s$. In the later part of the paper, will also investigate necessary and sufficient conditions needed for the upper bound to hold.
Co-Authors Chula Jayawardene