Supereulerian Digraphs with Large Arc‐Strong Connectivity

Algefari, Mansour J.; Lai, Hong‐Jian

doi:10.1002/jgt.21885

Cited by 14 publications

(7 citation statements)

References 15 publications

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“…In [6], Bang-Jensen and Maddaloni proved that if ( ) ≥ ( ) for a graph , then is supereulerian. In [1], Algefari and Lai proved that if ( ) ≥ ′ ( ) for a strong digraph , then is supereulerian. It has been observed that when studying the supereulerian problem, the lower bound of a degree condition to warrant a supereulerian graph may be reduced by about half for bipartite graphs, as seen in Theorem 5 [19].…”

Section: (I)mentioning

confidence: 99%

“…(See Figure 2, where unoriented edges represents a directed 2-cycle.) Let  1 ( , ) be the family of all digraphs isomorphic to one of such 1…”

Section: Mechanismsmentioning

confidence: 99%

“…In , Bang‐Jensen and Maddaloni proved that if

λ (G) \geq α (G)

for a graph G , then G is supereulerian. In , Algefari and Lai proved that if

λ false(D false) \geq α^{'} false(D false)

for a strong digraph D , then D is supereulerian.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier studies were done by Gutin [14,15]. Some of the recent developments can be found in [1][2][3]6,16,17], among others. In particular, the following have been proved.…”

Section: Introductionmentioning

confidence: 99%

“…In the proof of Claim 1, we use the notation of Definition 3.2, as depicted in Figure 4. By Definition 3.2 (iii-a) and (iii-b), 1…”

mentioning

confidence: 99%

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Supereulerian bipartite digraphs

Zhang

Liu

Wang

et al. 2018

Journal of Graph Theory

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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 λ(D) of a digraph D is not less than the independence number α(D), then D is supereulerian. A digraph is bipartite if its underlying graph is bipartite. Let α′false(Dfalse) be the size of a maximum matching of D. We prove that if D is a bipartite digraph satisfying λfalse(Dfalse)≥⌊α′(D)2⌋+1, then D is supereulerian. Consequently, every bipartite digraph D satisfying λfalse(Dfalse)≥⌊αfalse(Dfalse)2⌋+1 is supereulerian. The bound of our main result is best possible.

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Section: (I)mentioning

confidence: 99%

“…(See Figure 2, where unoriented edges represents a directed 2-cycle.) Let  1 ( , ) be the family of all digraphs isomorphic to one of such 1…”

Section: Mechanismsmentioning

confidence: 99%

“…In , Bang‐Jensen and Maddaloni proved that if

λ (G) \geq α (G)

for a graph G , then G is supereulerian. In , Algefari and Lai proved that if

λ false(D false) \geq α^{'} false(D false)

for a strong digraph D , then D is supereulerian.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier studies were done by Gutin [14,15]. Some of the recent developments can be found in [1][2][3]6,16,17], among others. In particular, the following have been proved.…”

Section: Introductionmentioning

confidence: 99%

“…In the proof of Claim 1, we use the notation of Definition 3.2, as depicted in Figure 4. By Definition 3.2 (iii-a) and (iii-b), 1…”

mentioning

confidence: 99%

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