The authors verify the Hilton-Zhao conjecture that splitting a vertex in an n-vertex connected regular Class 1 graph with Δ(G) ≥ (2n-2)/3 produces an edge-chromatic critical graph.
Holyer,The NP-completeness of edge-coloring, SIAM J
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On the Hilton-Zhao vertex-splitting conjecture
The authors verify the Hilton-Zhao conjecture that splitting a vertex in an n-vertex connected regular Class 1 graph with Δ(G) ≥ (2n-2)/3 produces an edge-chromatic critical graph.