Abstract
For a finite graph G, we study the maximum 2-edge colorable subgraph problem and a related ratio , where is the matching number of G, and is the size of the largest matching in any pair of disjoint matchings maximizing (equivalently, forming a maximum 2-edge colorable subgraph). Previously, it was shown that , and the class of graphs achieving 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 among all graphs that can be covered by a certain choice of a maximum matching and H, as above.
Citation
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
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