Minimally contraction-critically 6-connected graphs
暂无分享,去创建一个
An edge of a 6-connected graph is said to be removable (resp. contractible) if the removal (resp. contraction) of the edge results in a 6-connected graph. A 6-connected graph is said to be minimally contraction-critically 6-connected if it has neither removable edge nor contractible edge. Let x be a vertex of a minimally contraction-critically 6-connected graph G. In this paper, we show that there is one of some specified configurations around x and using this result we prove that x has a neighbor of degree 6. We also display a condition for x to have at least two neighbors of degree 6.
[1] Li Min. VERTICES OF DEGREE 6 IN A CONTRACTION-CRITICAL 6 CONNECTED GRAPH , 2005 .
[2] Nicola Martinov. Uncontractable 4-connected graphs , 1982, J. Graph Theory.
[3] Ken-ichi Kawarabayashi,et al. Vertices of degree 6 in a contraction critically 6-connected graph , 2003, Discret. Math..
[4] William T. Tutte,et al. A theory of 3-connected graphs , 1961 .
[5] W. Mader. Ecken vom Gradn in minimalenn-fach zusammenhängenden Graphen , 1972 .