2012/09/11 by Kuo‐Ching Huang, Kuo-Ching Huang, Huang, Kuo-Ching +3
Computer Science · Mathematics · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C15
paper · pdf · doi:10.48550/arxiv.1209.2202
arxiv created 2012/09/11 · openalex publication_date 2012/09/11 · arxiv updated 2012/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a simple graph. A coloring of vertices of G is called (i) a 2-proper coloring if vertices at distance 2 receive distinct colors; (ii) an injective coloring if vertices possessing a common neighbor receive distinct colors; (iii) a square coloring if vertices at distance at most 2 receive distinct colors. In this paper, we study inequalities of Nordhaus-Guddam type for the 2-proper chromatic number, the injective chromatic number, and the square chromatic number.