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Solitude patterns of $r$-graphs via CLM's dependence relation
Recently, Goedgebeur, Mazzuoccolo, Renders, Wolf and the second author [Cubic graphs with edges in exactly one perfect matching, J. Graph Theory 112 (2026), 276-289] proved that every $3$-connected $3$-regular graph has at most six solitary edges; an edge is solitary if it participates in precisely
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