The strong chromatic index of graphs and subdivisions

Nakprasit, Keaitsuda Maneeruk; Nakprasit, Kittikorn

doi:10.1016/j.disc.2013.11.005

Cited by 4 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conjecture 2.2 was verified by Steger and Yu [21]. Conjecture 2.4 was confirmed by Wu and Lin [22] and was generalized by Nakprasit and Nakprasit [18]. The previously mentioned result of Borodin and Ivanova [2] verified Conjecture 2.6 for planar graphs.…”

Section: 6mentioning

confidence: 68%

Strong chromatic index of subcubic planar multigraphs

Kostochka

Ruksasakchai

et al. 2016

European Journal of Combinatorics

View full text Add to dashboard Cite

Abstract. The strong chromatic index of a multigraph is the minimum k such that the edge set can be k-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gyárfás, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.This paper is to appear in European J. Combin. 51 (2016) 380-397.Mathematics Subject Classification: 05C15 (05C10)

show abstract

Section: 6mentioning

confidence: 68%

Strong chromatic index of subcubic planar multigraphs

Kostochka

Ruksasakchai

et al. 2016

European Journal of Combinatorics

View full text Add to dashboard Cite

show abstract

“…In this case, the coloring is usually called strong edge coloring (see e.g. [6,9,12,14,15,18]). The main results are related to the computational complexity of the problem in classes of graphs.…”

Section: Introductionmentioning

confidence: 99%

On the complexity of the flow coloring problem

Campêlo

Huiban

Rodrigues

et al. 2015

Discrete Applied Mathematics

View full text Add to dashboard Cite

a b s t r a c tMotivated by bandwidth allocation under interference constraints in radio networks, we define and investigate an optimization problem that combines the classical flow and edge coloring problems in graphs. Let G = (V , E) be a graph with a demand function b : V → Z + and a gateway gis a set with one flow for each source node. Every flow φ defines a multigraph G φ with vertex set V and all edges in the paths in φ. A distance-d edge coloring of a flow φ is an edge coloring of G φ such that two edges with the same color are at distance at least d in G. The distance-d flow coloring problem (FCP d ) is the problem of obtaining a flow φ on G with a distance-d edge coloring where the number of used colors is minimum. For any fixed d ≥ 3, we prove that FCP d is NP-hard even on a bipartite graph with just one source node. For d = 2, we also prove NP-hardness on a bipartite graph with multiples sources. For d = 1, we show that the problem is polynomial in 3-connected graphs and bipartite graphs. Finally, we show that a list version of the problem is inapproximable in polynomial time by a factor of O(log n) even on n-vertex paths, for any d ≥ 1.

show abstract

“…The conjecture is still open, and see [2,4,10,16,17] for some recent partial results. We remark that in [10,17], it was shown that the conjecture holds if a = 2 or 3.…”

Section: Introductionmentioning

confidence: 99%

On incidence choosability of cubic graphs

Kang

Park

2019

Discrete Mathematics

View full text Add to dashboard Cite

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. *

show abstract

The strong chromatic index of graphs and subdivisions

Cited by 4 publications

References 9 publications

Strong chromatic index of subcubic planar multigraphs

Strong chromatic index of subcubic planar multigraphs

On the complexity of the flow coloring problem

On incidence choosability of cubic graphs

Contact Info

Product

Resources

About