Degree sum conditions for path-factor uniform graphs

A spanning subgraph of a graph G is called a path-factor of G if its each component is a path. A path-factor is called a P ≥ k -factor of G if its each component admits at least k vertices, where k ≥ 2 . A graph G is called a P ≥ k -factor uniform graph if for any two different edges e 1 and e 2 of...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 55; no. 4; pp. 1409 - 1415
Main Author Dai, Guowei
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 01.12.2024
Springer Nature B.V
Subjects
Apexes
Applications of Mathematics
Graph theory
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
05C70
Graph
Path-factor
Degree sum
factor uniform graph
05C38
Online AccessGet full text
ISSN0019-5588
0975-7465
DOI10.1007/s13226-023-00446-7

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Summary:A spanning subgraph of a graph G is called a path-factor of G if its each component is a path. A path-factor is called a P ≥ k -factor of G if its each component admits at least k vertices, where k ≥ 2 . A graph G is called a P ≥ k -factor uniform graph if for any two different edges e 1 and e 2 of G , G admits a P ≥ k -factor containing e 1 and avoiding e 2 . The degree sum of G is defined by σ k ( G ) = min X ⊆ V ( G ) { ∑ x ∈ X d G ( x ) : X is an independent set of k vertices } . In this paper, we give two degree sum conditions for a graph to be a P ≥ 2 -factor uniform graph and a P ≥ 3 -factor uniform graph, respectively.
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ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00446-7