For relaxed DP-coloring, Sribunhung et al. proved that planar graphs without 4- and 7-cycles are DP-(0, 2, 2)-colorable. Li et al. proved that planar graphs without 4, 8-cycles or 4, 9-cycles are DP-(1, 1, 1)-colorable. Lu and Zhu proved that planar graphs without 4, 5-...
DP-coloring is a generalization of list-coloring, which was introduced by Dvo谩k and Postle. Zhang showed that every planar graph with neither adjacent triangles nor 5-, 6-, 9-cycles is 3-choosable. Liu et al. showed that every planar graph without 4-, 5-, 6- and 9-cycles is DP-...
Three-coloring Klein bottle graphs of girth five Let us remark that there are no 4-critical graphs of girth at least five on the projective plane and the torus [10] and on the Klein bottle =-=[9]-=-. The only non-planar surface for which the 3-colorability problem for ... R ...
DP-3-coloring of some planar graphsList coloringDP-coloringPlanar graphsIn this article, we use a unified approach to prove several classes of planar graphs are DP-3-colorable, which extend the corresponding results on 3-choosability. (C) 2018 Elsevier B.V. All rights reserved.Liu, Runrun...
Runrun Liu, Sarah Loeb, Yuxue Yin, Gexin Yu, DP-3-coloring of some planar graphs, arXiv:1802.09312.R. Liu, S. Loeb, Y. Yin, G. Yu, DP-3-coloring of some planar graphs, arXiv:1802.09312.R. Liu, S. Loeb, Y. Yin, G. Yu, DP-3-coloring of some planar graphs, Preprint, ar...
Planar graphs without 4-cycles adjacent to triangles are DP-4-colorable, arXiv:1712.08999, 2019; Sittitrai and Nakprasit, Every planar graph without i-cycles adjacent simultaneously to j-cycles and k-cycles is DP-4-colorable when { i , j , k } = { 3 , 4 , 5 } , arXiv:1801.06760...
Planar graphs without 4-cycles adjacent to triangles are DP-4-colorable,arXiv:1712.08999,2019; Sittitrai and Nakprasit, Every planar graph withouti-cycles adjacent simultaneously toj-cycles andk-cycles is DP-4-colorable when{i,j,k}={3,4,5}\\documentclass[12pt]{minimal} \\usepackage{amsmat...
DP-coloring (also known as correspondence coloring) introduced by Dvor谩k and Postle (2015) is a generalization of list coloring. In 2019, Chen et al. showed that planar graphs without [Formula: see text]-cycles adjacent to [Formula: see text]-cycles are DP-[Formula: see text]-colorable...
DP-coloring (also known as correspondence coloring) introduced by Dvor谩k and Postle (2015) is a generalization of list coloring. In 2019, Chen et al. showed that planar graphs without 4 -cycles adjacent to k -cycles are DP- 4 -colorable for k = 5 and 6. In thi...
Planar graphsIt is known that DP-coloring is a generalization of 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-(k,d)-coloring which is a generalization of a (k,d)-list coloring. We...