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A note on vertex-criticality with respect to edge-coloring

Cailing Wang

Abstract



Multigraphs for which the chromatic index achieving the maximum degree are said to be Class 1, and otherwise they are Class 2. The problem of characterizing graphs of Class 1 or Class 2 is NP-hard, so it is natural to study graphs which are critical. There are a number of denitions of criticality concerning the chromatic index and some interesting problems arising from them. In this paper, we improve a result on the vertex criticality of edge-coloring of star multigraphs.

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