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Critical Graphs for R(Pn, Pm) and the Star-Critical Ramsey Number for Paths

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Hook J.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 4

689-701

The graph Ramsey number R(G,H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H. The star-critical Ramsey number r∗(G,H) is the smallest integer k such that every 2-coloring of the edges of Kr − K1,r−1−k contains either a red copy of G or a blue copy of H. We will classify the critical graphs, 2-colorings of the complete graph on R(G,H) − 1 vertices with no red G or blue H, for the path-path Ramsey number. This classification will be used in the proof of r∗(Pn, Pm).

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1 Discussiones Mathematicae Graph Theory

1 Hook J.

1 2015

Wyniki wyszukiwania

Critical Graphs for R(Pn, Pm) and the Star-Critical Ramsey Number for Paths