Vertex-deleted subgraphs and regular factors from regular graph
Hongliang Lu, Bing Bai, Wei Wang

TL;DR
This paper investigates conditions under which the removal of any vertex from a specific class of regular, edge-connected graphs guarantees the existence of a k-factor in the resulting subgraph.
Contribution
It provides new sufficient conditions ensuring that vertex-deleted subgraphs of certain regular graphs contain a k-factor, extending previous results in graph factor theory.
Findings
Identifies conditions guaranteeing k-factors after vertex removal
Extends known results for regular, edge-connected graphs
Applicable to graphs with odd order and specific regularity
Abstract
Let , and be three integers such that . Let be a -regular, -edge-connected graph of odd order. We obtain some sufficient conditions, which guarantee contains a -factor for all .
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Limits and Structures in Graph Theory
