Tools for studying paths and cycles in digraphs
β Scribed by Delorme, C.; Ordaz, O.; Quiroz, D.
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 251 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
β¦ Synopsis
The main goal of this work was to describe the basic elements constituting a specialized knowledge base in the field of paths and circuits in digraphs. This knowledge base contains commented on examples with textual and graphical descriptions, invariants, relations among invariants, and theorems. It used as a ''kernel'' of the AGORA interactive system, for assisting a graph researcher in the mental process of constructing and studying conjectures in the mentioned specialized field.
π SIMILAR VOLUMES
## Abstract Let ${\cal G}$ be a fixed set of digraphs. Given a digraph __H__, a ${\cal G}$βpacking in __H__ is a collection ${\cal P}$ of vertex disjoint subgraphs of __H__, each isomorphic to a member of ${\cal G}$. A ${\cal G}$βpacking ${\cal P}$ is __maximum__ if the number of vertices belonging
## Abstract We show that a directed graph of order __n__ will contain __n__βcycles of every orientation, provided each vertex has indegree and outdegree at least (1/2 + __n__^β1/6^)__n__ and __n__ is sufficiently large. Β© 1995 John Wiley & Sons, Inc.
We extend an elegant proof technique of A . G . Thomason, and deduce several parity theorems for paths and cycles in graphs. For example, a graph in which each vertex is of even degree has an even number of paths if and only if it is of even order, and a graph in which each vertex is of odd degree h
We define a matrix A associated with an acyclic digraph 1, such that the coefficient of z j in det(I+zA) is the number of j-vertex paths in 1. This result is actually a special case of a more general weighted version.
Given two integers n and k, n β₯ k > 1, a k-hypertournament T on n vertices is a pair (V, A), where V is a set of vertices, |V | = n and A is a set of k-tuples of vertices, called arcs, so that for any k-subset S of V, A contains exactly one of the k! k-tuples whose entries belong to S. A 2-hypertour