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Related Experiment Video

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Generating Strictly Controlled Stimuli for Figure Recognition Experiments

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Published on: March 18, 2019

Vertex-deleted subgraphs and regular factors from regular graph.

Hongliang Lu¹, Wei Wang, Bing Bai

¹Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China.

Discrete Mathematics

|October 11, 2011

Summary

This summary is machine-generated.

This study provides sufficient conditions for a graph G to contain a k-factor after removing any vertex. These findings are crucial for understanding graph factorization properties in regular, edge-connected graphs.

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Area of Science:

Graph theory
Combinatorics
Discrete mathematics

Background:

Graph factorization is a fundamental concept in graph theory.
Understanding the properties of factors in regular and edge-connected graphs is essential.

Purpose of the Study:

To establish sufficient conditions for the existence of a k-factor in a graph after vertex deletion.
To analyze the impact of vertex removal on the k-factorability of specific graph classes.

Main Methods:

The study considers a 2r-regular, 2m-edge-connected graph G of odd order.
Conditions are derived for the subgraph G-v (G with vertex v removed) to possess a k-factor.

Main Results:

Sufficient conditions are obtained for G-v to contain a k-factor for any vertex v in G.
The results generalize and extend existing theorems in graph factorization.

Conclusions:

The derived conditions provide valuable insights into the structural properties of graphs related to k-factorization.
This research contributes to the ongoing study of graph properties under vertex deletion.