Connectedness and Hamiltonicity of graphs on vertex colorings

McDonald, Daniel C.

doi:10.48550/arxiv.1507.05344

Cited by 2 publications

(2 citation statements)

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“…A 2-tree is obtained from a triangle by repeatedly adding a new vertex that is joined to the end vertices of an existing edge. McDonald [McD15] considers a variation that allows recoloring more than one vertex at a time, namely at most ℓ vertices at a time, and he asked for the minimum ℓ for which the resulting flip graph has a Hamilton cycle.…”

Section: Vertex Coloringsmentioning

confidence: 99%

Combinatorial Gray Codes — an Updated Survey

Mütze

2023

Electron. J. Combin.

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A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a `small change'. Such listings are known for many different combinatorial objects, including bitstrings, combinations, permutations, partitions, triangulations, but also for objects defined with respect to a fixed graph, such as spanning trees, perfect matchings or vertex colorings. This survey provides a comprehensive picture of the state-of-the-art of the research on combinatorial Gray codes. In particular, it gives an update on Savage's influential survey [C. D. Savage. A survey of combinatorial Gray codes. SIAM Rev., 39(4):605--629, 1997.], incorporating many more recent developments. We also elaborate on the connections to closely related problems in graph theory, algebra, order theory, geometry and algorithms, which embeds this research area into a broader context. Lastly, we collect and propose a number of challenging research problems, thus stimulating new research endeavors.

show abstract

Section: Vertex Coloringsmentioning

confidence: 99%

Combinatorial Gray Codes — an Updated Survey

Mütze

2023

Electron. J. Combin.

View full text Add to dashboard Cite

show abstract

“…A 2-tree is obtained from a triangle by repeatedly adding a new vertex that is joined to the end vertices of an existing edge. McDonald [McD15] considers a variation that allows recoloring more than one vertex at a time, namely at most vertices at a time, and he asked for the minimum for which the resulting flip graph has a Hamilton cycle.…”

Section: P57mentioning

confidence: 99%

Combinatorial Gray codes-an updated survey

Mütze¹

2022

Preprint

View full text Add to dashboard Cite

A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a 'small change'. Such listings are known for many different combinatorial objects, including bitstrings, combinations, permutations, partitions, triangulations, but also for objects defined with respect to a fixed graph, such as spanning trees, perfect matchings or vertex colorings. This survey provides a comprehensive picture of the state-of-the-art of the research on combinatorial Gray codes. In particular, it gives an update on Savage's influential survey [C. D. Savage. A survey of combinatorial Gray codes. SIAM Rev., 39(4):605-629, 1997.], incorporating many more recent developments. We also elaborate on the connections to closely related problems in graph theory, algebra, order theory, geometry and algorithms, which embeds this research area into a broader context. Lastly, we collect and propose a number of challenging research problems, thus stimulating new research endeavors.

show abstract

Connectedness and Hamiltonicity of graphs on vertex colorings

Cited by 2 publications

References 10 publications

Combinatorial Gray Codes — an Updated Survey

Combinatorial Gray Codes — an Updated Survey

Combinatorial Gray codes-an updated survey

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