Cycle covers (III) – Compatible circuit decomposition and K5-transition minor

Fleischner, Herbert; Gh., Behrooz Bagheri; Zhang, Cun-Quan; Zhang, Zhang

doi:10.1016/j.jctb.2018.11.008

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…For planar eulerian graphs G one can prove a more general result than the SC Conjecture; namely it suffices to assume that the transition system is non-separating; one even has a compatible cycle decomposition (CCD) in an arbitrary eulerian graph G if the given transition system in G is non-separating and does not yield a SUD-K 5 −minor 1 . This has been shown recently in [9].…”

Section: Introductionsupporting

confidence: 62%

“…We note explicitly that the compatible cycle decomposition problem has been verified for planar graphs by Fleischner [6], for K 5 −minor-free graphs by Fan and Zhang [3], and for SUD-K 5 −minor-free graphs by Fleischner et al [9].…”

Section: Introductionmentioning

confidence: 63%

“…All concepts not defined in this paper can be found in [1,5,9], giving preference to a definition as stated in [5] if it differs from the corresponding definition in [1]. A cycle Sabidussi's Compatibility Conjecture (SC Conjecture) Given a connected eulerian graph G with δ(G) > 2 and an eulerian trail T ǫ of G, there is a cycle decomposition S of G such that edges consecutive in T ǫ belong to different elements in S. Whence one calls S compatible with T ǫ .…”

Section: Introductionmentioning

confidence: 99%

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Perfect Pseudo-Matchings in cubic graphs

Fleischner,

Gh.,

Klocker

2019

Preprint

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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 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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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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Perfect Pseudo-Matchings in cubic graphs

Fleischner,

Gh.,

Klocker

2019

Preprint

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A SAT Approach for Finding Sup-Transition-Minors

Klocker

Fleischner

Raidl

2020

Lecture Notes in Computer Science

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Perfect Pseudo-Matchings in Cubic Graphs

Fleischner,

Gh,

Klocker

2024

Graphs and Combinatorics

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A M in a cubic graph G is a spanning subgraph of G such that every component of M is isomorphic to $$K_2$$ K 2 or to $$K_{1,3}$$ K 1 , 3 . In view of snarks G with dominating cycle C, this is a natural generalization of perfect matchings since $$G \setminus E(C)$$ G \ E ( C ) is a perfect pseudo-matching. Of special interest are such M where 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 $$5-$$ 5 - edge-connected snarks.

show abstract

Cycle covers (III) – Compatible circuit decomposition and K5-transition minor

Cited by 4 publications

References 12 publications

Perfect Pseudo-Matchings in cubic graphs

Perfect Pseudo-Matchings in cubic graphs

A SAT Approach for Finding Sup-Transition-Minors

Perfect Pseudo-Matchings in Cubic Graphs

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