Abstract
AbstractLet be a multigraph with maximum degree , chromatic index , and total chromatic number . The total coloring conjecture proposed by Behzad and Vizing, independently, states that for a multigraph , where is the multiplicity of . Moreover, Goldberg conjectured that if and noticed the conjecture holds when is an edge‐chromatic critical graph. By assuming the Goldberg–Seymour conjecture, we show that if in this note. Consequently, if and has a spanning edge‐chromatic critical subgraph.
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