On incidence coloring conjecture in Cartesian products of graphs

Gregor, Petr; Lužar, Borut; Soták, Roman

doi:10.1016/j.dam.2016.04.030

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…Incidence colourings were first introduced and studied by Brualdi and Quinn Massey [2]. Incidence colourings of various graph families have attracted much interest in recent years, see for instance [3,4,6,7,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Strong incidence colouring of graphs

Benmedjdoub¹,

Sopena²

2024

Discuss. Math. Graph Theory

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An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f ) of G are adjacent whenever (i) v = w, or (ii) e = f , or (iii) vw = e or f . An incidence p-colouring of G is a mapping from the set of incidences of G to the set of colours {1, . . . , p} such that every two adjacent incidences receive distinct colours. Incidence colouring has been introduced by Brualdi and Quinn Massey in 1993 and, since then, studied by several authors.In this paper, we introduce and study the strong version of incidence colouring, where incidences adjacent to the same incidence must also get distinct colours. We determine the exact value of -or upper bounds onthe strong incidence chromatic number of several classes of graphs, namely cycles, wheel graphs, trees, ladder graphs, square grids and subclasses of Halin graphs.

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Section: Introductionmentioning

confidence: 99%

Strong incidence colouring of graphs

Benmedjdoub¹,

Sopena²

2024

Discuss. Math. Graph Theory

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Section: Introductionmentioning

confidence: 99%

Incidence choosability of graphs

Benmedjdoub

Bouchemakh

Sopena

2019

Discrete Applied Mathematics

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An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f ) of G are adjacent whenever (i) v = w, or (ii) e = f , or (iii) vw = e or f . An incidence p-colouring of G is a mapping from the set of incidences of G to the set of colours {1, . . . , p} such that every two adjacent incidences receive distinct colours. Incidence colouring has been introduced by Brualdi and Quinn Massey in 1993 and, since then, studied by several authors.In this paper, we introduce and study the list version of incidence colouring. We determine the exact value of -or upper bounds on -the incidence choice number of several classes of graphs, namely square grids, Halin graphs, cactuses and Hamiltonian cubic graphs.

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“…Hence, every cubic graph has incidence chromatic number 4 or 5, and it is known to be NP-hard to determine if the incidence chromatic number of a cubic graph is 4 (see [12,13]). See [7,8,11,15,20,21] for some interesting families of graphs whose incidence chromatic numbers are known.…”

Section: Introductionmentioning

confidence: 99%

On incidence choosability of cubic graphs

Kang

Park

2019

Discrete Mathematics

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An incidence of a graph G is a pair (u, e) where u is a vertex of G and e is an edge of G incident with u. Two incidences (u, e) and (v, f ) of G are adjacent whenever (i) u = v, or (ii) e = f , or (iii) uv = e or uv = f . An incidence k-coloring of G is a mapping from the set of incidences of G to a set of k colors such that every two adjacent incidences receive distinct colors. The notion of incidence coloring has been introduced by Brualdi and Quinn Massey (1993) from a relation to strong edge coloring, and since then, attracted by many authors.On a list version of incidence coloring, it was shown by Benmedjdoub et. al. (2017) that every Hamiltonian cubic graph is incidence 6-choosable. In this paper, we show that every cubic (loopless) multigraph is incidence 6-choosable. As a direct consequence, it implies that the list strong chromatic index of a (2, 3)-bipartite graph is at most 6, where a (2,3)-bipartite graph is a bipartite graph such that one partite set has maximum degree at most 2 and the other partite set has maximum degree at most 3. *

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On incidence coloring conjecture in Cartesian products of graphs

Cited by 10 publications

References 15 publications

Strong incidence colouring of graphs

Strong incidence colouring of graphs

Incidence choosability of graphs

On incidence choosability of cubic graphs

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