共查询到20条相似文献,搜索用时 15 毫秒
1.
It is known that planar graphs without cycles of length 4, i, j, or 9 with 4<i<j<9, except that i=7 and j=8, are 3-choosable. This paper proves that planar graphs without cycles of length 4, 7, 8, or 9 are also 3-choosable. 相似文献
2.
Yingqian Wang 《Discrete Mathematics》2010,310(1):147-373
It is shown that a planar graph without cycles of length 4, 5, 8, or 9 is 3-choosable. 相似文献
3.
Wei-fan WANG~ Min CHEN Department of Mathematics Zhejiang Normal University Jinhua China 《中国科学A辑(英文版)》2007,50(11):1552-1562
In this paper we prove that every planar graph without 4,6 and 8-cycles is 3-colorable. 相似文献
4.
In this paper, we mainly prove that planar graphs without 4-, 7- and 9-cycles are 3-colorable. 相似文献
5.
6.
A graph G is edge-L-colorable, if for a given edge assignment L={L(e):e∈E(G)}, there exists a proper edge-coloring ? of G such that ?(e)∈L(e) for all e∈E(G). If G is edge-L-colorable for every edge assignment L with |L(e)|≥k for e∈E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph with maximum degree Δ(G)≠5 and without adjacent 3-cycles, or with maximum degree Δ(G)≠5,6 and without 7-cycles, then G is edge-(Δ(G)+1)-choosable. 相似文献
7.
8.
《Discrete Mathematics》2022,345(9):112942
A graph G is k-degenerate if every subgraph of G has a vertex with degree at most k. Using the Euler's formula, one can obtain that planar graphs without 3-cycles are 3-degenerate. Wang and Lih, and Fijav? et al. proved the analogue results for planar graphs without 5-cycles and planar graphs without 6-cycles, respectively. Recently, Liu et al. showed that planar graphs without 3-cycles adjacent to 5-cycles are 3-degenerate. In this work, we generalized all aforementioned results by showing that planar graphs without mutually adjacent 3-,5-, and 6-cycles are 3-degenerate. A graph G without mutually adjacent 3-,5-, and 6-cycles means that G cannot contain three graphs, say , and , where is a 3-cycle, is a 5-cycle, and is a 6-cycle such that each pair of , and are adjacent. As an immediate consequence, we have that every planar graph without mutually adjacent 3-,5-, and 6-cycles is DP-4-colorable. This consequence also generalizes the result by Chen et al that planar graphs without 5-cycles adjacent to 6-cycles are DP-4-colorable. 相似文献
9.
Planar graphs without 5-cycles or without 6-cycles 总被引:1,自引:0,他引:1
Let G be a planar graph without 5-cycles or without 6-cycles. In this paper, we prove that if G is connected and δ(G)≥2, then there exists an edge xy∈E(G) such that d(x)+d(y)≤9, or there is a 2-alternating cycle. By using the above result, we obtain that (1) its linear 2-arboricity , (2) its list total chromatic number is Δ(G)+1 if Δ(G)≥8, and (3) its list edge chromatic number is Δ(G) if Δ(G)≥8. 相似文献
10.
In Thomassen (1995) [4], Thomassen proved that planar graphs of girth at least 5 are 3-choosable. In Li (2009) [3], Li improved Thomassen’s result by proving that planar graphs of girth 4 with no 4-cycle sharing a vertex with another 4- or 5-cycle are 3-choosable. In this paper, we prove that planar graphs of girth 4 with no 4-cycle sharing an edge with another 4- or 5-cycle are 3-choosable. It is clear that our result strengthens Li’s result. 相似文献
11.
It is proved that planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable. 相似文献
12.
Some structural properties of planar graphs without 4-cycles are investigated. By the structural properties, it is proved that every planar graph G without 4-cycles is edge-(Δ(G)+1)-choosable, which perfects the result given by Zhang and Wu: If G is a planar graph without 4-cycles, then G is edge-t-choosable, where t=7 if Δ(G)=5, and otherwise t=Δ(G)+1. 相似文献
13.
Total colorings and list total colorings of planar graphs without intersecting 4-cycles 总被引:1,自引:0,他引:1
Suppose that G is a planar graph with maximum degree Δ and without intersecting 4-cycles, that is, no two cycles of length 4 have a common vertex. Let χ″(G), and denote the total chromatic number, list edge chromatic number and list total chromatic number of G, respectively. In this paper, it is proved that χ″(G)=Δ+1 if Δ≥7, and and if Δ(G)≥8. Furthermore, if G is a graph embedded in a surface of nonnegative characteristic, then our results also hold. 相似文献
14.
Min Chen 《Discrete Mathematics》2008,308(24):6216-6225
A proper vertex coloring of a graph G=(V,E) is acyclic if G contains no bicolored cycle. A graph G is acyclically L-list colorable if for a given list assignment L={L(v):v∈V}, there exists a proper acyclic coloring π of G such that π(v)∈L(v) for all v∈V. If G is acyclically L-list colorable for any list assignment with |L(v)|≥k for all v∈V, then G is acyclically k-choosable. In this paper we prove that every planar graph without 4-cycles and without two 3-cycles at distance less than 3 is acyclically 5-choosable. This improves a result in [M. Montassier, P. Ochem, A. Raspaud, On the acyclic choosability of graphs, J. Graph Theory 51 (2006) 281-300], which says that planar graphs of girth at least 5 are acyclically 5-choosable. 相似文献
15.
《Discrete Mathematics》2022,345(4):112790
DP-coloring of graphs as a generalization of list coloring was introduced by Dvo?ák and Postle (2018). In this paper, we show that every planar graph without intersecting 5-cycles is DP-4-colorable, which improves the result of Hu and Wu (2017), who proved that every planar graph without intersecting 5-cycles is 4-choosable, and the results of Kim and Ozeki (2018). 相似文献
16.
17.
Xiangwen Li 《Discrete Mathematics》2009,309(8):2424-417
Let G be a plane graph of girth at least 4. Two cycles of G are intersecting if they have at least one vertex in common. In this paper, we show that if a plane graph G has neither intersecting 4-cycles nor a 5-cycle intersecting with any 4-cycle, then G is 3-choosable, which extends one of Thomassen’s results [C. Thomassen, 3-list-coloring planar graphs of girth 5, J. Combin. Theory Ser. B 64 (1995) 101-107]. 相似文献
18.
《Discrete Mathematics》2023,346(1):113192
Steinberg conjectured in 1976 that every planar graph with no cycles of length four or five is 3-colorable. This conjecture is disproved by constructing a planar graph with no cycles of length four or five but intersecting triangles. Jin et al. proved that plane graphs without 4- and 5-cycles and without ext-triangular 7-cycles are 3-colorable [SIAM J. Discrete Math. 31 (3) (2017) 1836–1847]. In this paper, we point out a mistake of their proof and give an improved proof. 相似文献
19.
Edge choosability and total choosability of planar graphs with no 3-cycles adjacent 4-cycles 总被引:1,自引:0,他引:1
Two cycles are said to be adjacent if they share a common edge. Let G be a planar graph without triangles adjacent 4-cycles. We prove that if Δ(G)≥6, and and if Δ(G)≥8, where and denote the list edge chromatic number and list total chromatic number of G, respectively. 相似文献
20.
Hua Cai 《数学学报(英文版)》2015,31(12):1951-1962
A k-total-coloring of a graph G is a coloring of vertices and edges of G using k colors such that no two adjacent or incident elements receive the same color.In this paper,it is proved that if G is a planar graph with Δ(G) ≥ 7 and without chordal 7-cycles,then G has a(Δ(G) + 1)-total-coloring. 相似文献