Restricted Size Ramsey Number for Matching versus Tree and Triangle Unicyclic Graphs of Order Six

Elda Safitri, Peter John, Denny Riama Silaban

Abstract


Let F, G, and H be simple graphs. The graph F arrows (G,H) if for any red-blue coloring on the edge of F, we find either a red-colored graph G or a blue-colored graph H in F. The Ramsey number r(G,H) is the smallest positive integer r such that a complete graph Kr arrows (G,H). The restricted size Ramsey number r∗(G,H) is the smallest positive integer r∗ such that there is a graph F, of order r(G,H) and with the size r∗, satisfying F arrows (G,H). In this paper we give the restricted size Ramsey number for a matching of two edges versus tree and triangle unicyclic graphs of order six.

Keywords


restricted size Ramsey number; matching graph; tree graph; triangle unicyclic graph

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References


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DOI: http://dx.doi.org/10.12962/j24775401.v8i1.10817

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International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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