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A digraph D is supereulerian if D has a spanning closed ditrail. Bang‐Jensen and Thomassé conjectured that if the arc‐strong connectivity of a digraph D is not less than the independence number , then D is supereulerian. A digraph is bipartite if its underlying graph is bipartite. Let be the size of a maximum matching of D. We prove that if D is a bipartite digraph satisfying ...
A classical result of Chvátal and Erdös says that the graph G with connectivity κ(G) not less than its independence number α(G) (i.e. κ(G)≥α(G)) is Hamiltonian. In this paper, we show that the 2-connected graph G with κ(G)≥α(G)−1 is one of the following: supereulerian, the Petersen graph, the 2-connected graph with three vertices of degree two obtained from K2,3 by replacing a vertex of degree three...
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