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

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Bielak H., Dąbrowska K.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2015

tom 69

nr 2

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 \(\overline{F}\) contains \(H\) as a subgraph, where \(\overline{F}\) 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 of order \(n\) with at least one edge.

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1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Bielak H.

1 Dąbrowska K.

1 2015

Wyniki wyszukiwania

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