论文信息 - A note on the list vertex arboricity of toroidal graphs

A note on the list vertex arboricity of toroidal graphs

Abstract The vertex arboricity a ( G ) of a graph G is the minimum number of colors required to color the vertices of G such that no cycle is monochromatic. The list vertex arboricity a l ( G ) is the list-coloring version of this concept. In this note, we prove that if G is a toroidal graph, then a l ( G ) ≤ 4 ; and a l ( G ) = 4 if and only if G contains K 7 as an induced subgraph.

Min Chen | Wei-Fan Wang | Yiqiao Wang

[1] Hudson V. Kronk,et al. An Analogue to the Heawood Map‐Colouring Problem , 1969 .

[2] Wei-Fan Wang,et al. On the vertex-arboricity of planar graphs without 7-cycles , 2012, Discret. Math..

[3] Alexandr V. Kostochka,et al. Variable degeneracy: extensions of Brooks' and Gallai's theorems , 2000, Discret. Math..

[4] Haihui Zhang,et al. Vertex arboricity of toroidal graphs with a forbidden cycle , 2014, Discret. Math..

[5] André Raspaud,et al. On the vertex-arboricity of planar graphs , 2008, Eur. J. Comb..

[6] H. Zhang. On list vertex 2-arboricity of toroidal graphs without cycles of specific length , 2016 .

[7] Min Chen,et al. Toroidal graphs without 3-cycles adjacent to 5-cycles have list vertex-arboricity at most 2 , 2015 .

[8] Min Chen,et al. List vertex-arboricity of toroidal graphs without 4-cycles adjacent to 3-cycles , 2016, Discret. Math..

[9] S. L. Hakimi,et al. A Note on the Vertex Arboricity of a Graph , 1989, SIAM J. Discret. Math..

[10] Yuan Jinjiang,et al. On the vertex arboricity of planar graphs of diameter two , 2007 .

[11] Gary Chartrand,et al. The point-arboricity of a graph , 1968 .

[12] Min Chen,et al. Vertex-arboricity of planar graphs without intersecting triangles , 2012, Eur. J. Comb..

[13] John Mitchem,et al. Critical Point‐Arboritic Graphs , 1975 .