Abstract:An edge of a matching covered graph G is a forcing edge if it lies in precisely one perfect matching of G. A matching covered graph is a brick if and only if it is 3-connected and bicritical (the deletion of each pair of distinct vertices results in a graph with a perfect matching). In this paper, we prove that every vertex of a brick is incident with a forcing edge if and only if the brick is an odd wheel up to multiple edges.
From: Yaxian Zhang [view email]
[v1]
Thu, 25 Jun 2026 04:39:17 UTC (164 KB)
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