The extended graphs

An algorithm finding the shortest path joining two given vertices in an extended graph has been studied in other papers. In this paper, we show that the algorithm presented in doesn’t work for the extended graphs in. We define the other extended graph, called an extended weighted graph, such that a similar algorithm works for it.

8p tamynhan8 04-11-2020 9 1   Download

A subset M  E(G) of the edge set E(G) of a graph G is called a matching provided that no two edges in M have a vertex in common. A perfect matching M is a matching with the property that each vertex of G is incident with an edge in M. For k a positive integer, a graph G is k-extendable provided that G has a matching of size k and every matching in G of size at most k can be extended to a perfect matching in G.

15p thulanh6 14-09-2011 57 4   Download

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Bar´at and Hajnal on this subject and develop a generalization we call restricted arcwidth.

18p thulanh5 12-09-2011 56 4   Download