W-state graphs are precisely the matching-covered graphs with specific half-edge colorings whose 3-connected components are W-cones, enabling efficient recognition and ruling out simple graphs.
Vardi and Zhiwei Zhang
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W-state graphs: Structure and Algorithms
W-state graphs are precisely the matching-covered graphs with specific half-edge colorings whose 3-connected components are W-cones, enabling efficient recognition and ruling out simple graphs.