Supereulerian digraphs

Supereulerian digraphs

A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. We give a necessary condition for a digraph to be supereulerian first and then characterize the digraphDwhich are not supereulerian under the condition that δ(D)+δ(D) ≥ |V (D)|−4. © 2014 Elsevier B.V. All rights reserved.

Supereulerian digraphs with given local structures

Connected (g, f)-factors and supereulerian digraphs

Given a digraph (an undirected graph, resp.) D and two positive integers f (x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)-factor if g(x) d + H (x) = d ? H (x) f (x)(g(x) d H (x) f (x), resp.) for every x 2 V (D). If f (x) = g(x) = 1 for every x, then a connected (g; f)-factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for ...

Supereulerian Digraphs with Large Arc-Strong Connectivity

Let D be a digraph and let λ(D) be the arc-strong connectivity of D, and α′(D) be the size of a maximum matching of D. We proved that if λ(D) ≥ α′(D) > 0, then D has a spanning eulerian subdigraph. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 81: 393–402, 2016

Ore-type degree condition of supereulerian digraphs

A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. Hong et al. proved that δ(D) + δ(D) ≥ |V (D)| − 4 implies D is supereulerian except some well-characterized digraph classes if the minimum degree is large enough. In this paper, we characterize the digraphs D which are not supereulerian under the condition d+D (u) + d−D (v) ≥ |V (D)| − 4 for any pair of vertices u an...