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April 2022 Characterization of saturated graphs related to pairs of disjoint matchings
Zhengda Mo, Sam Qunell, Anush Tserunyan, Jenna Zomback
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Illinois J. Math. 66(1): 59-77 (April 2022). DOI: 10.1215/00192082-9719963

Abstract

For a finite graph G, we study the maximum 2-edge colorable subgraph problem and a related ratio μ(G)ν(G), where ν(G) is the matching number of G, and μ(G) is the size of the largest matching in any pair (H,H) of disjoint matchings maximizing |H|+|H| (equivalently, forming a maximum 2-edge colorable subgraph). Previously, it was shown that 45μ(G)ν(G)1, and the class of graphs achieving 45 was completely characterized. In this paper, we first show that graph decompositions into paths and even cycles provide a new way to study these parameters. We then use this technique to characterize the graphs achieving μ(G)ν(G)=1 among all graphs that can be covered by a certain choice of a maximum matching and H, H as above.

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Zhengda Mo. Sam Qunell. Anush Tserunyan. Jenna Zomback. "Characterization of saturated graphs related to pairs of disjoint matchings." Illinois J. Math. 66 (1) 59 - 77, April 2022. https://doi.org/10.1215/00192082-9719963

Information

Received: 27 January 2021; Revised: 21 December 2021; Published: April 2022
First available in Project Euclid: 14 February 2022

Digital Object Identifier: 10.1215/00192082-9719963

Subjects:
Primary: 05C70

Rights: Copyright © 2022 by the University of Illinois at Urbana–Champaign

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Vol.66 • No. 1 • April 2022
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