1. Three Results on Cycle-Wheel Ramsey Numbers.
- Author
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Zhang, Yanbo, Broersma, Hajo, and Chen, Yaojun
- Subjects
RAMSEY numbers ,SUBGRAPHS ,GENERALIZATION ,COMBINATORICS ,GRAPH theory ,MATHEMATICAL analysis - Abstract
Given two graphs $$G_1$$ and $$G_2$$ , the Ramsey number $$R(G_1, G_2)$$ is the smallest integer $$N$$ such that, for any graph $$G$$ of order $$N$$ , either $$G_1$$ is a subgraph of $$G$$ , or $$G_2$$ is a subgraph of the complement of $$G$$ . We consider the case that $$G_1$$ is a cycle and $$G_2$$ is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels versus cycles of even order; and large cycles versus generalized odd wheels. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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