منابع مشابه
Counting Paths in Graphs
We give a simple combinatorial proof of a formula that extends a result by Grigorchuk [Gri78a, Gri78b] (rediscovered by Cohen [Coh82]) relating cogrowth and spectral radius of random walks. Our main result is an explicit equation determining the number of ‘bumps’ on paths in a graph: in a d-regular (not necessarily transitive) non-oriented graph let the series G(t) count all paths between two f...
متن کاملBalanced Paths in Colored Graphs
We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which bounds the difference between the occurrences of any two colors for all prefixes of the path. These two not...
متن کاملShortest Paths In Unweighed Graphs
When dealing with shortest paths in weighed or unweighed graphs, one may solve one-to-one, one-to-all or all-to-all instances. But the known algorithms compute one single shortest path of the considered instance. This article describes a new algorithm (patent pending) designed to compute all the shortest paths between two vertices of a directed, strongly connected and unweighed graph G, contain...
متن کاملHamilton Paths in Grid Graphs
A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for general grid graphs is shown to be NP-co...
متن کاملDisjoint paths in sparse graphs
We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg, Vazirani and Yannakakis [Primal-dual approximation algorithms for integral flow and multicut in trees, Algorithmica 18 (1997) 3–20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other classical generalizations of trees. We also introduce the k-edge-o...
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: Opuscula Mathematica
سال: 2019
ISSN: 1232-9274
DOI: 10.7494/opmath.2019.39.6.829