This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63
(1995), 153–158), who proved that the list edge chromatic numberχ′ list (G) of a bipartite …

After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

arXiv:2210.05915v2 [math.CO] 22 Apr 2023 Page 1 arXiv:2210.05915v2 [math.CO] 22 Apr
2023 Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) …

The central problem of the total-colorings is the total-coloring conjecture, which asserts that
every graph of maximum degree Δ admits a (Δ+2)-total-coloring. Similar to edge-colorings …

Total chromatic number of planar graphs with maximum degree ten Page 1 Total Chromatic
Number of Planar Graphs with Maximum Degree Ten Weifan Wang DEPARTMENT OF …

It is proved that ifGis a planar graph with total (vertex–edge) chromatic number χ ″,
maximum degree Δ and girthg, then χ ″= Δ+ 1 if Δ≥ 5 andg≥ 5, or Δ≥ 4 andg≥ 6, or Δ≥ …

It was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum
degree Δ are entirely (Δ+ 4)-colourable, ie, the vertices, edges, and faces of a simple plane …

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), χl′(G) and χl ″(G) …

In the paper, we prove that if G is a graph embeddable on a surface of Euler characteristic ε<
0 and Δ≥ 25− 24ε+ 10, then χlist′(G)= Δ and χlist ″(G)= Δ+ 1. This extends a result of …

The Total Coloring Conjecture, in short, TCC, says that every simple graph is (Δ+ 2)-totally-
colorable where Δ is the maximum degree of the graph. Even for planar graphs this …