an:00568834
Zbl 0792.05113
Sheehan, John
Graph decomposition with constraints on connectivity and minimum degree
EN
Capobianco, Michael F. (ed.) et al., Graph theory and its applications: East and West. Proceedings of the first China-USA international conference, held in Jinan, China, June 9-20, 1986. New York: New York Academy of Sciences,. Ann. N. Y. Acad. Sci. 576, 480-486 (1989).
1989
a
05C70 05C40 05C35
decomposition; connectivity; minimum degree; spanning bipartite graph; balanced spanning bipartite subgraph; partition
A classic argument due to Erd??s shows that every finite graph \(G\) with minimum degree \(\delta(G) \geq \delta\) contains a spanning bipartite graph \(H\) with \(\delta (H) \geq | \overline {\delta/2} |\). Jackson has proved that if \(\delta (G) \geq \delta \geq 2\), then there exists a balanced spanning bipartite subgraph \(H\) with \(\delta(H) \geq 1\). \textit{C. Thomassen} [J. Graph Theory 7, 165-167 (1983; Zbl 0515.05045)], developing the Erd??s argument, proved that every finite graph \(G\) with \(\delta (G) \geq 12k\) contains a partition \((X,Y)\) of \(V(G)\) such that \(\delta (X) \geq k\) and \(\delta (Y) \geq k\). We discuss in this paper an, at least superficially, related question that arose from our interest [\textit{R. J. Faudree} and \textit{J. Sheehan}, Discrete Math. 46, 151-157 (1983; Zbl 0518.05047)] in size Ramsey numbers.
For the entire collection see [Zbl 0788.00046].
Zbl 0515.05045; Zbl 0518.05047