Counting paths in digraphs
نویسندگان
چکیده
منابع مشابه
Counting paths in digraphs
We begin with some terminology. All digraphs in this paper are finite. For a digraph G, we denote its vertex and edge sets by V (G) and E(G), respectively. Unless otherwise stated, we assume |V (G)| = n. The members of E(G) are ordered pairs of vertices. We use the notation uv to denote an ordered pair of vertices (u, v) (whether or not u and v are adjacent). We only consider digraphs which hav...
متن کاملA Matrix for Counting Paths in Acyclic Digraphs
We will define a matrix A=A1 associated with an acyclic digraph 1, such that the coefficients of the characteristic polynomial of A enumerate the paths in 1 according to their length. Our result is actually an easy consequence of a more general theorem of Goulden and Jackson, but this special case seems never to have been explicitly noted before. We will give two simple proofs, the first of whi...
متن کاملPacking paths in digraphs
Let G be a xed collection of digraphs. Given a digraph H, a Gpacking of H is a collection of vertex disjoint subgraphs of H, each isomorphic to a member of G. A G-packing, P, is maximum if the number of vertices belonging to some member of P is maximum, over all G-packings. The analogous problem for undirected graphs has been extensively studied in the literature. We concentrate on the cases wh...
متن کاملCovering digraphs by paths
The problems of miniiiwn Lg.: ana minimum vertex covers by paths results relate to papers by Galki-M&ram, Meyniel, Alspach-Pullman and mait resulti is contimed with partially ordered sets. are discussed. The others. One of tie NM+oak The terminology is rather standard, generally following Berge [3]. In any case where ar&iguity may arise we give +finiticns. Graphs alnd digraphs are f@ite, except...
متن کاملDisjoint Paths in Symmetric Digraphs
Given a number of requests `, we propose a polynomial-time algorithm for finding ` disjoint paths in a symmetric directed graph. It is known that the problem of finding ` ≥ 2 disjoint paths in a directed graph is NP-hard [S. Fortune, J. Hopcroft, J. Wyllie, The directed subgraph homeomorphism problem, Journal of Theoretical Computer Science 10 (2) (1980) 111–121]. However, by studying minimal s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.05.008