The strong chromatic index of graphs with edge weight eight

Chen, Lily; Chen, Shumei; Zhao, Ren; Zhou, Xiangqian

doi:10.1007/s10878-020-00582-4

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, the bound of 10 is tight and the bound of 15 is two larger than the conjectured bound of 13. For graphs with edge weight 8, Chen, Chen, Zhao and Zhou [2] gave an upper bound of 21 (recall that the conjectured bound is 20), which is a natural extension of the current best bound 21 for graphs with maximum degree 4 in [12] as each such graph has edge weight 8. An induced subgraph of G isomorphic to the complete bipartite graph K 1,3 is called a claw of G. And a graph is called claw-free if it has no claw.…”

Section: Introductionmentioning

confidence: 92%

Strong chromatic index of claw-free graphs with edge weight seven

Lin¹,

Lin²

2024

Discuss. Math. Graph Theory

View full text Add to dashboard Cite

Let G be a graph and k a positive integer. A strong k-edge-coloring of G is a mapping φ : E(G) → {1, 2, . . . , k} such that for any two edges e and e that are either adjacent to each other or adjacent to a common edge, φ(e) = φ(e ). The strong chromatic index of G is the minimum integer k such that G has a strong k-edge-coloring. The edge weight of G is defined to be max{d(u) + d(v) : uv ∈ E(G)}, where d(v) denotes the degree of v in G. In this paper, we prove that every claw-free graph with edge weight at most 7 has strong chromatic index at most 9, which is sharp.

show abstract

Section: Introductionmentioning

confidence: 92%