2018/01/20 by Pongpat Sittitrai, Sittitrai, Pongpat, Kittikorn Nakprasit +1
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1801.06760
openalex publication_date 2018/01/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
DP-coloring is a generalization of a list coloring in simple graphs. Many\nresults in list coloring can be generalized in those of DP-coloring. Kim and\nOzeki showed that planar graphs without k-cycles where k=3,4,5, or 6 are\nDP-4-colorable. Recently, Kim and Yu extended the result on 3- and\n4-cycles by showing that planar graphs without triangles adjacent to\n4-cycles are DP-4-colorable. Xu and Wu showed that planar graphs without\n5-cycles adjacent simultaneously to 3-cycles and 4-cycles are\n4-choosable. In this paper, we extend the result on 5-cycles and triangles\nadjacent to 4-cycles by showing that planar graphs without i-cycles\nadjacent simultaneously to j-cycles and k-cycles are DP-4-colorable when\n i,j,k = 3,4,5 . This also generalizes the result of Xu and Wu.\n