Geodesic
Dominated pair degree sum conditions of supereulerian digraphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 879-891

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A digraph D is supereulerian if D contains a spanning eulerian subdigraph. In this paper, we propose the following problem: is there an integer t with 0≤ t≤ n-3 so that any strong digraph with n vertices satisfying either both d(u) ≥ n -1+ t and d(v) ≥ n-2- t or both d(u) ≥ n-2- t and d(v) ≥ n -1+ t, for any pair of dominated or dominating nonadjacent vertices {u, v}, is supereulerian? We prove the cases when t=0,t=n-4 and t=n-3. Moreover, we show that if a strong digraph D with n vertices satisfies min{d^+(u) + d^- (v), d^- (u) + d^+(v)}≥ n-1 for any pair of dominated or dominating nonadjacent vertices {u,v} of D, then D is supereulerian.
Keywords: supereulerian digraph, spanning eulerian subdigraph, dominated pair degree sum condition 
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Dong, Changchang; Meng, Jixiang; Liu, Juan. Dominated pair degree sum conditions of supereulerian digraphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 879-891. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a3/