Exact Values for Some Size Ramsey Numbers of Paths and Cycles
For the graphs G1, G2, and G, if every 2-coloring (red and blue) of the edges of G results in either a copy of blueG1 or a copy of redG2, we write G → (G1, G2). The size Ramsey number R^(G1,G2) is the smallest number e such that there is a graph G with size e satisfying G → (G1, G2), i.e., R^(G1,G2)...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-09-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2020.00350/full |
| Summary: | For the graphs G1, G2, and G, if every 2-coloring (red and blue) of the edges of G results in either a copy of blueG1 or a copy of redG2, we write G → (G1, G2). The size Ramsey number R^(G1,G2) is the smallest number e such that there is a graph G with size e satisfying G → (G1, G2), i.e., R^(G1,G2)=min{|E(G)|:G→(G1,G2)}. In this paper, by developing the procedure and algorithm, we determine exact values of the size Ramsey numbers of some paths and cycles. More precisely, we obtain that R^(C4,C5)=19, R^(C6,C6)=26, R^(P4,C5)=14, R^(P4,P5)=10, R^(P4,P6)=14, R^(P5,P5)=11, R^(P3,P5)=7 and R^(P3,P6)=8. |
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| ISSN: | 2296-424X |