Inherited Properties of Descendants

Baniasadi, Pouya; Ejov, Vladimir; Filar, Jerzy A.; Haythorpe, Michael

doi:10.1007/978-3-319-19680-0_2

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…Therefore, in Γ * g,3 , each subgraph functions equivalently to a vertex, and therefore the Petersen graph shares its non-Hamiltonicity with Γ * g,3 . An alternative proof using results Baniasadi and Haythorpe [2] arises from noticing that Γ * g,3 has the non-Hamiltonian Petersen graph as an ancestor gene, violating the necessary condition for Γ * g,3 to be Hamiltonian. Lemma 3.2.…”

Section: Non-bridge Constructionsmentioning

confidence: 99%

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

Haythorpe¹

2019

Preprint

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It is well known that 3-regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3-regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1-, 2-or 3-edge-connected depending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3-regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness.

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Section: Non-bridge Constructionsmentioning

confidence: 99%

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

Haythorpe¹

2019

Preprint

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“…Since it is not possible to visit all three subgraphs with a simple cycle, the graph is non-Hamiltonian. An alternative proof of non-Hamiltonicity for graphs of this type is given in Baniasadi and Haythorpe [2].…”

Section: Non-bridge Constructionsmentioning

confidence: 99%

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

Haythorpe¹

2014

ujam

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Inherited Properties of Descendants

Cited by 2 publications

References 12 publications

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

Non-Hamiltonian 3-Regular Graphs with Arbitrary Girth

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