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The Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths

Halina BielakKinga Dąbrowska — 2015

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

The Ramsey number R ( G , H ) for a pair of graphs G and H is defined as the smallest integer n such that, for any graph F on n vertices, either F contains G or F ¯ contains H as a subgraph, where F ¯ denotes the complement of F . We study Ramsey numbers for some subgraphs of generalized wheels versus cycles and paths and determine these numbers for some cases. We extend many known results studied in [5, 14, 18, 19, 20]. In particular we count the numbers R ( K 1 + L n , P m ) and R ( K 1 + L n , C m ) for some integers m , n , where L n is a linear forest...

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