Object
Title: On maximum matchings in almost regular graphs
Abstract:
In 2010, Mkrtchyan, Petrosyan, and Vardanyan proved that every graph G with 2≤δ(G)≤Δ(G)≤3 contains a maximum matching M such that no two vertices uncovered by M share a neighbor, where Δ(G) and δ(G) denote the maximum and minimum degrees of vertices in G, respectively. In the same paper they suggested the following conjecture: every graph G with Δ(G)−δ(G)≤1 contains a maximum matching M such that no two vertices uncovered by M share a neighbor. Recently, Picouleau disproved this conjecture by constructing a bipartite counterexample G with Δ(G)=5 and δ(G)=4. In this note, we show that the conjecture is false for graphs G with Δ(G)−δ(G)=1 and Δ(G)≥4, and for r-regular graphs when r≥7.
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oai:noad.sci.am:136139
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Institute for Informatics and Automation Problems
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- Digital Library > Academic Insitutions > Insitute for Informatics and Automation Problems of NAS RA > Publications
Last modified:
Apr 19, 2021
In our library since:
Apr 19, 2021
Number of object content hits:
22
All available object's versions:
https://noad.sci.am/publication/149553
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| Edition name | Date |
|---|---|
| Petros A.Petrosyan, On maximum matchings in almost regular graphs | Apr 19, 2021 |
