Cycles and paths in edge‐colored graphs with given degrees

Abouelaoualim, A.; Das, Kinkar Ch.; Véga, W. Fernandez de la; Karpiński, Marek; Manoussakis, Yannis; Martinhon, Carlos A. J.; Saad, Rachid

doi:10.1002/jgt.20440

Cited by 28 publications

(67 citation statements)

References 16 publications

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“…The following interesting result and conjecture were obtained by Abouelaoualim, Das, Fernandez de la Vega, Karpinski, Manoussakis, Martinhon and Saad [1]. …”

Section: Long Pc Cycles and Pathsmentioning

confidence: 58%

Properly Coloured Cycles and Paths: Results and Open Problems

Gutin

Kim

2009

Graph Theory, Computational Intelligence and Thought

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In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph G into an ordinary graph that allow us to check the existence of PC cycles and PC (s, t)-paths in G and, if they exist, to find shortest ones among them. We raise a problem of finding the optimal transformation and consider a possible solution to the problem.

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“…The following interesting result and conjecture were obtained by Abouelaoualim, Das, Fernandez de la Vega, Karpinski, Manoussakis, Martinhon and Saad [1]. …”

Section: Long Pc Cycles and Pathsmentioning

confidence: 58%

Properly Coloured Cycles and Paths: Results and Open Problems

Gutin

Kim

2009

Graph Theory, Computational Intelligence and Thought

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“…Many other results for edge-coloured multigraphs can be found in the survey by Bang-Jensen and Gutin [2]. Results involving only degree conditions can be found in [1].…”

Section: Introductionmentioning

confidence: 88%

“…Thus by a theorem in [1], G c has a proper Hamiltonian cycle and so a proper Hamiltonian path. Consider now G c − {x}.…”

Section: -Edge-coloured Multigraphsmentioning

confidence: 99%

Proper Hamiltonian Paths in Edge-Coloured Multigraphs

Águeda

Borozan

Groshaus

et al. 2017

Graphs and Combinatorics

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Given a c-edge-coloured multigraph, a proper Hamiltonian path is a path that contains all the vertices of the multigraph such that no two adjacent edges have the same colour. In this work we establish sufficient conditions for an edge-coloured multigraph to guarantee the existence of a proper Hamiltonian path, involving various parameters as the number of edges, the number of colours, the rainbow degree and the connectivity.

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“…Many other results for edge-colored multigraphs can be found in the survey by Bang-Jensen and Gutin [3]. Results involving only degree conditions can be found in [1].…”

Section: Introductionmentioning

confidence: 92%

Proper Hamiltonian cycles in edge-colored multigraphs

Águeda

Borozan

Díaz

et al. 2017

Discrete Mathematics

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A c-edge-colored multigraph has each edge colored with one of the c available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges have the same color. In this work we establish sufficient conditions for a multigraph to have a proper Hamiltonian cycle, depending on several parameters such as the number of edges and the rainbow degree.

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Cycles and paths in edge‐colored graphs with given degrees

Cited by 28 publications

References 16 publications

Properly Coloured Cycles and Paths: Results and Open Problems

Properly Coloured Cycles and Paths: Results and Open Problems

Proper Hamiltonian Paths in Edge-Coloured Multigraphs

Proper Hamiltonian cycles in edge-colored multigraphs

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