Perfect Pseudo-Matchings in cubic graphs

Perfect Pseudo-Matchings in cubic graphs

A perfect pseudo-matching M in a cubic graph G is a spanning subgraph of G such that every component of M is isomorphic to K_2 or to K_1,3. In view of snarks G with dominating cycle C, this is a natural generalization of perfect matchings since G-E(C) is a perfect pseudo-matching. Of special interes...

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Veröffentlicht in:arXiv.org 2019-05
Hauptverfasser: Fleischner, Herbert, Behrooz Bagheri Gh, Klocker, Benedikt
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Graph theory
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description A perfect pseudo-matching M in a cubic graph G is a spanning subgraph of G such that every component of M is isomorphic to K_2 or to K_1,3. In view of snarks G with dominating cycle C, this is a natural generalization of perfect matchings since G-E(C) is a perfect pseudo-matching. Of special interest are such M where the graph G/M is planar because such G have a cycle double cover. We show that various well known classes of snarks contain planarizing perfect pseudo-matchings, and that there are at least as many snarks with planarizing perfect pseudo-matchings as there are cyclically 5-edge-connected snarks.
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title Perfect Pseudo-Matchings in cubic graphs
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