On Cycles through Vertices of Large Semidegree in Digraphs
S.Kh. Darbinyan, I.A. Karapetyan

TL;DR
This paper proves that in certain strong digraphs with a cycle of length n-1, there exists a cycle passing through all vertices with large in-degree and out-degree, except for some extremal cases.
Contribution
It establishes a new condition linking near-maximum cycles to large-degree vertices in strong digraphs of odd order.
Findings
Existence of a cycle containing all high-degree vertices under given conditions
Characterization of extremal cases where the cycle does not include all such vertices
Extension of cycle structure understanding in strong digraphs
Abstract
Let be a strong digraph on vertices. In this paper we show that if contains a cycle of length , then has also a cycle which contains all vertices with in-degree and out-degree at least (unless some extremal cases).
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory
