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.
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The maximum Pfaffian number over graphs of genus at most g is at least (8/3)^g, improving prior linear lower bounds to exponential for bipartite and complete graphs.
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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.
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Exponential Lower Bounds for the Pfaffian Number of Graphs
The maximum Pfaffian number over graphs of genus at most g is at least (8/3)^g, improving prior linear lower bounds to exponential for bipartite and complete graphs.