On the core of a unicyclic graph - Levit, Vadim E. (Ars mathematica contemporanea, 2012)
A set ?$S \subseteq V$? is independent in a graph ?$G = (V, E)$? if no two vertices from ?$S$? are adjacent. By core?$(G)$? we mean the intersection of all maximum independent sets. The independence number ?$α(G)$? is the cardinality of a maximum independent set, while ?$μ(G)$? is the size of a maximum matching in ?$G$?. A connected graph having only one cycle, say ?$C$?, is a unicyclic graph. In this paper we prove that if ?$G$? is a unicyclic graph of order ?$n$? and T$n - 1 = α(G) + μ(G)$T, then core?$(G)$? coincides with the union of cores of all trees in ?$G - C$?.
Keywords: core; enociklični graf; graph theory; jedro grafa; König-Egervárijev graf; König-Egerváry graph; maksimalna neodvisna množica; matching; maximum independent set; prirejanje; teorija grafov; unicyclic graph