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Injective edge chromatic number of sparse graphs.
- Source :
-
Applied Mathematics & Computation . Jul2024, Vol. 473, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- A k -edge coloring ϕ of graph G is injective if any two edges at distance 2 or in the same triangle get different colors. The minimum k in such an edge coloring is the injective edge chromatic number of G , written as χ i ′ (G). We prove in this paper that for any graph G with Δ (G) ≤ 5 , χ i ′ (G) ≤ 18 if m a d (G) < 16 5 , χ i ′ (G) ≤ 19 if m a d (G) < 7 2 and χ i ′ (G) ≤ 20 if m a d (G) < 15 4. • The results obtained in this paper enrich the previous work concerning on the study of injective coloring of sparse graphs. • The discharging method used in this paper is especially useful to solve the problem of injective coloring. • Some important reducible configurations are presented and the discharging rulers are well designed. • It is the first time to study the sufficient conditions for graphs with maximum degree Δ = 5 satisfying χ i ′ (G) ≤ Δ (Δ − 1). [ABSTRACT FROM AUTHOR]
- Subjects :
- *SPARSE graphs
*INJECTIVE functions
*GRAPH coloring
*PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 473
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 176500290
- Full Text :
- https://doi.org/10.1016/j.amc.2024.128668