A Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs
Abstract
Bang-Jensen-Gutin-Li type conditions are degree conditions for the existence of hamiltonian cycles in digraphs, which impose degree restrictions on nonadjacent vertices which have a common in-neighbor or a common out-neighbor. They can be viewed as directed analogues of both Fan-type conditions and heavy subgraph conditions in undirected graphs, and they also generalized the classes of locally semicomplete digrahs, loclaly in-semicomplete digraphs, and locally out-semicomplete digraphs. In this paper, we prove what is, to our knowledge, the first Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs. More precisely, let D be a strong digraph with order n≥ 3. We show that, if for every u∈ V(D) belonging to a dominated nonadjacent pair or a dominating nonadjacent pair, we have d(u)≥ n, then D is pancyclic, unless D belongs to one of two well-characterized classes of exceptional digraphs.
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BibTeX
@misc{li2026bangjensengutinli,
title = {{A Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs}},
author = {Tianyue Li and Zanbo Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35063},
eprint = {2610.35063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35063},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs
AU - Tianyue Li
AU - Zanbo Zhang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35063
UR - https://arxiv.org/abs/2610.35063
AB - Bang-Jensen-Gutin-Li type conditions are degree conditions for the existence of hamiltonian cycles in digraphs, which impose degree restrictions on nonadjacent vertices which have a common in-neighbor or a common out-neighbor. They can be viewed as directed analogues of both Fan-type conditions and heavy subgraph conditions in undirected graphs, and they also generalized the classes of locally semicomplete digrahs, loclaly in-semicomplete digraphs, and locally out-semicomplete digraphs. In this paper, we prove what is, to our knowledge, the first Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs. More precisely, let D be a strong digraph with order n≥ 3. We show that, if for every u∈ V(D) belonging to a dominated nonadjacent pair or a dominating nonadjacent pair, we have d(u)≥ n, then D is pancyclic, unless D belongs to one of two well-characterized classes of exceptional digraphs.
ER -