A degree condition of 2-factors in bipartite graphs

Extensions to 2-Factors in Bipartite Graphs

A graph is d-bounded if its maximum degree is at most d. We apply the Ore– Ryser Theorem on f -factors in bipartite graphs to obtain conditions for the extension of a 2-bounded subgraph to a 2-factor in a bipartite graph. As consequences, we prove that every matching in the 5-dimensional hypercube extends to a 2-factor, and we obtain conditions for this property in general regular bipartite gra...

C4–free 2-factors in bipartite graphs

D. Hartvigsen [H] recently gave an algorithm to find a C4–free 2–factor in a bipartite graph and using this algorithm he proved several nice theorems. Now we give a simple inductive proof for a generalization of his Tutte-type theorem, and prove the corresponding Ore-type theorem as well. The proof follows the idea of the inductive proof for the Hall’s theorem given by Halmos and Vaughn [HV].

A Degree Condition For Graphs to Have Connected (g, f)-Factors

On 2-factors containing 1-factors in bipartite graphs

Moon and Moser (Israel J. Math. 1 (1962) 163-165) showed that if G is a balanced bipartite graph of order 2n and minimum degree 0>~(n + 1)/2, then G is hamiltonian. Recently, it was shown that their well-known degree condition also implies the existence of a 2-factor with exactly k cycles provided n~> max{52,2k -~ + 1}. In this paper, we show that a similar degree condition implies that for eac...

Signed degree sets in signed bipartite graphs

A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of ...