Almost well-dominated bipartite graphs with minimum degree at least two

On perfect matchings in random bipartite graphs with minimum degree at least two

Diameter Two Graphs of Minimum Order with Given Degree Set

The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...

An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three

We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G = Gδ≥3 n,m. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n) time and succeeds w.h.p.

Domination in Graphs of Minimum Degree at least Two and Large Girth

We prove that for graphs of order n, minimum degree δ ≥ 2 and girth g ≥ 5 the domination number γ satisfies γ ≤ ( 1 3 + 2 3g ) n. As a corollary this implies that for cubic graphs of order n and girth g ≥ 5 the domination number γ satisfies γ ≤ ( 44 135 + 82 135g ) n which improves recent results due to Kostochka and Stodolsky (An upper bound on the domination number of n-vertex connected cubic...

diameter two graphs of minimum order with given degree set

the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for ...