Arc-disjoint in-trees in directed graphs
スポンサーリンク
概要
- 論文の詳細を見る
Given a directed graph D = (V,A) with a set of d specified vertices S = {s 1,…, s d } ⊆ V and a function f: S → ℕ where ℕ denotes the set of natural numbers, we present a necessary and sufficient condition such that there exist Σ i=1 d f(s i ) arc-disjoint in-trees denoted by T i,1,T i,2,…, $$ T_{i,f(s_0 )} $$ for every i = 1,…,d such that T i,1,…,$$ T_{i,f(s_0 )} $$ are rooted at s i and each T i,j spans the vertices from which s i is reachable. This generalizes the result of Edmonds [2], i.e., the necessary and sufficient condition that for a directed graph D=(V,A) with a specified vertex s∈V, there are k arc-disjoint in-trees rooted at s each of which spans V. Furthermore, we extend another characterization of packing in-trees of Edmonds [1] to the one in our case.
論文 | ランダム
- としての形式主義文学論争(1)内容と他者をめぐって
- 無力であることへの予感、無為であることへの嫌悪--志賀直哉初期作品と
- 樋口一葉『うもれ木』論--森鴎外訳『埋木』・幸田露伴『風流仏』『一口剣』との連関
- の力、だけが見る夢--志賀直哉『いたづら』とその映画化をめぐって
- 〈殺人〉の居場所--志賀直哉『范の犯罪』覚書