A short proof of the versatile version of Fleischner’s theorem

Müttel, Janina; Rautenbach, Dieter

doi:10.1016/j.disc.2012.07.032

Cited by 12 publications

(7 citation statements)

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“…Fairly recent development in hamiltonian graph theory has shown a resurgence of interest in hamiltonian cycles and paths in the square of 2-connected graphs (which we call 2-blocks for short). In particular, short proofs have been found for two results of the second author of the present paper, [10,11]. And more recently, in [1] the authors develop algorithms which are linear in |E(G)| and produce a hamiltonian cycle, a hamiltonian path joining arbitrary vertices u and v respectively, in G 2 .…”

Section: Introductionmentioning

confidence: 81%

A best possible result for the square of a 2-block to be hamiltonian

Ekstein

Fleischner

2021

Discrete Mathematics

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Section: Introductionmentioning

confidence: 81%

A best possible result for the square of a 2-block to be hamiltonian

Ekstein

Fleischner

2021

Discrete Mathematics

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“…The result by Fleischner in [6] concerning the existence of a hamiltonian cycle (a [2,2]-factor) in the square of 2-connected graph is well known. Recently, Müttel and Rautenbach in [12] gave a shorter proof of this result. Theorem 1.…”

Section: Introductionmentioning

confidence: 90%

Connected Even Factors in the Square of Essentially 2-Edge-connected Graph

Ekstein

Xiong

2017

Electron. J. Combin.

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An essentially k-edge connected graph G is a connected graph such that deleting less than k edges from G cannot result in two nontrivial components. In this paper we prove that if an essentially 2-edgeconnected graph G satisfies that for any pair of leaves at distance 4 in G there exists another leaf of G that has distance 2 to one of them, then the square G 2 has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge-connected graph does not contain a connected even factor with bounded maximum degree.

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“…However, since the 1990's shorter proofs of what has become known as Fleischner's Theorem, were developed first byŘíha in [16] and later by Georgakopoulos in [11]. A short proof of an even stronger version of that theorem was proved by Müttel and Rautenbach in [13]. Unfortunately, the methods developed for these shorter proofs do not seem to suffice to prove the main result of this paper (Theorem 4).…”

Section: Introductionmentioning

confidence: 96%