We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...
It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for...
The old well-known result of Chartrand, Kaugars and Lick [1] says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G - v is still k-connec...