A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G
contains at least one vertex from S. Denote by ψ k (G) the minimum cardinality of a k-path …

For a graph G and S⊂ V (G), if G− S is acyclic, then S is said to be a decycling set of G. The
size of a smallest decycling set of G is called the decycling number of G. The purpose of this …

For a graph $ G $ and $ S\subset V (G) $, if $ GS $ is acyclic, then $ S $ is said to be a
decycling set of $ G $. The size of a smallest decycling set of $ G $ is called the decycling …

For a graph G, let τ (G) be the decycling number of G and c (G) be the number of vertex-
disjoint cycles of G. It has been proved that c (G)≤ τ (G)≤ 2 c (G) for an outerplanar graph …

所謂的消圈集或反饋點集, 是無向圖或有向圖裡的一個點集合, 滿足扣掉這個點集合後,
圖上沒有圈. 一個圖的消圈數是最小的消圈集的數目. 決定一個一般圖的消圈數已經被證明是NP …

A decycling set in a graph G is a set D of vertices such that G− D is acyclic. The decycling
number of G, φ (G), is the cardinality of a smallest decycling set in G. We obtain sharp …