Injective edge coloring of sparse graphs with maximum degree 5

Junlei Zhu (), Yuehua Bu and Hongguo Zhu
Additional contact information
Junlei Zhu: Jiaxing University
Yuehua Bu: Zhejiang Normal University
Hongguo Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 44, 10 pages

Abstract: Abstract A k-injective-edge coloring of a graph G is a mapping $$c:E(G)\rightarrow \{1,2,\cdots ,k\}$$ c : E ( G ) → { 1 , 2 , ⋯ , k } such that $$c(e_1)\ne c(e_3)$$ c ( e 1 ) ≠ c ( e 3 ) for any three consecutive edges $$e_1,e_2,e_3$$ e 1 , e 2 , e 3 of a path or a 3-cycle. $$\chi _{i}'(G)=\min \{k|G$$ χ i ′ ( G ) = min { k | G has a k-injective-edge coloring $$\}$$ } is called the injective chromatic index of G. In this paper, we prove that for graphs G with $$\Delta (G)\le 5$$ Δ ( G ) ≤ 5 , (1) $$\chi _{i}'(G)\le 8$$ χ i ′ ( G ) ≤ 8 if $$mad(G)

Keywords: Maximum degree; Maximum average degree; Injective edge coloring; 05C15 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-022-00972-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00972-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-022-00972-w

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().