The smallest integer k needed for the assignment of k colors to the elements so that the
coloring is proper (vertices and edges) is called the total chromatic number of a graph …

A total k-coloring of a graph G is a coloring of V (G)∪ E (G) using k colors such that no two
adjacent or incident elements receive the same color. The total chromatic number of G is the …

Total coloring of planar graphs with maximum degree 8 - ScienceDirect Skip to main contentSkip
to article Elsevier logo Journals & Books Help Search My account Sign in View PDF Download …

Let G be a planar graph with maximum degree Δ≥ 7 and without adjacent 4-cycles, that is,
two cycles of length 4 do not share one common edge. Then its total chromatic number is Δ+ …

Let GG be a planar graph with\varDelta ≥ 8 Δ≥ 8 and vv be a vertex of G G. It is proved that
χ''(G)=\varDelta+ 1 χ′′(G)= Δ+ 1 if vv is not incident with chordal 5 5-or 6 6-cycles by Shen …

The minimum number of colors needed to properly color the vertices and edges of a graph G
is called the total chromatic number of G and denoted by ζ ″(G). It is shown that if a planar …

Total coloring of graphs embedded in surfaces of nonnegative Euler characteristic Page 1
SCIENCE CHINA Mathematics . ARTICLES . January 2014 Vol.57 No.1: 211–220 doi …

While planar graphs are flat from a topological viewpoint, we observe that they are not from
a geometric one. We prove that every planar graph can be embedded into a surface …

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 …

The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+ 2)-
colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC …