Degree conditions of two vertices with distance two or three for the existence of a Hamilton cycle passing through a matching in a bipartite graph

In 1972, Las Vergnas gave a degree sum conditions for the existence of a perfect matching containing a given matching and for the existence of a Hamilton cycle passing through a given matching. In this paper, we investigate whether we can replace the degree sum conditions in the results due to Las V...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 41; no. 6; p. 118
Main Authors: Chiba, Shuya, Tsugaki, Masao, Yamashita, Tomoki, Yashima, Takamasa
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.12.2025
Springer Nature B.V
Subjects:
Apexes
Combinatorics
Engineering Design
Graph theory
Matching
Mathematics
Mathematics and Statistics
Original Paper
Theorems
Degree condition
05C70
Bipartite graph
Perfect matching
05C38
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary:In 1972, Las Vergnas gave a degree sum conditions for the existence of a perfect matching containing a given matching and for the existence of a Hamilton cycle passing through a given matching. In this paper, we investigate whether we can replace the degree sum conditions in the results due to Las Vergnas with degree conditions of two vertices with distance two or three.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-025-02978-7