EconPapers    
Economics at your fingertips  
 

2-Distance coloring of planar graphs without adjacent 5-cycles

Yuehua Bu, Zewei Zhang and Hongguo Zhu ()
Additional contact information
Yuehua Bu: Zhejiang Normal University
Zewei Zhang: Zhejiang Normal University
Hongguo Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 5, No 16, 19 pages

Abstract: Abstract The k-2-distance coloring of graph G is a mapping $$c:V(G)\rightarrow \{1,2,\ldots ,k\}$$ c : V ( G ) → { 1 , 2 , … , k } such that any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer k such that G has a k-2-distance coloring, denoted by $$\chi _{2}(G)$$ χ 2 ( G ) . In this paper, we prove that every planar graph G without adjacent 5-cycles and $$g(G)\ge 5$$ g ( G ) ≥ 5 and $$\Delta (G)\ge 17$$ Δ ( G ) ≥ 17 has $$\chi _{2}(G)\le \Delta +3$$ χ 2 ( G ) ≤ Δ + 3 .

Keywords: 2-Distance coloring; Planar graph; Girth; Cycle; 05C10; 05C15 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-023-01053-2 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:5:d:10.1007_s10878-023-01053-2

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

DOI: 10.1007/s10878-023-01053-2

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 ().

 
Page updated 2025-03-20
Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01053-2