Sufficient conditions on planar graphs to have a relaxed DP-3-colorability

2018/03/07 by Pongpat Sittitrai, Sittitrai, Pongpat, Kittikorn Nakprasit +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1803.03527

openalex publication_date 2018/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that DP-coloring is a generalization of a list coloring in simple graphs and many results in list coloring can be generalized in those of DP-coloring. In this work, we introduce a relaxed DP-coloring which is a generalization if a relaxed list coloring. We also shows that every planar graph G without 4-cycles or 6-cycles is DP-(k,d)^*-colorable. It follows immediately that G is (k,d)^*-choosable.

Citations

• A Sufficient condition for DP-4-colorability

Related

• DP-3-coloring of planar graphs without 4,9-cycles and two cycles from \5,6,7,8\
• DP-3-coloring of some planar graphs
• A Sufficient condition for DP-4-colorability
• Every planar graph without i-cycles adjacent simultaneously to\n j-cycles and k-cycles is DP-4-colorable when i,j,k = 3,4,5
• Planar graphs having no cycle of length 4, 6 or 8 are DP-3-colorable