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 χ ″ ( G ) ...
A k-total-coloring of a graph is a coloring of using k colors such that no two adjacent or incident elements receive the same color.
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 @g^''(G).
May 19, 2023 · In this paper, we present a proof that confirms the conjecture for graphs embeddable into a surface with non-negative Euler characteristic with maximum degree ...
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Feb 25, 2010 · 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 ...
Request PDF | Total coloring of planar graphs with maximum degree 8 | Let G be a planar graph with Δ⩾8Δ⩾8 and without adjacent cycles of size i and j, ...
ABSTRACT: The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar ...
Equitable coloring of planar graphs with maximum degree at least eight ; Article number, 113964 ; Journal, Discrete Mathematics ; Volume, 347 ; Issue number, 6.
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... More precisely, if G is a planar graph with ∆ ≥ 9, then χ t (G) = ∆(G) + 1. For planar graphs with maximum degree 7 or 8, some related results can be ...
Total coloring of planar graphs of maximum degree eight. The minimum number of colors needed to properly color the vertices and edges of a graph G is called ...