Showing papers on "Path graph published in 1975"
13 Oct 1975
TL;DR: In this article, a new algorithm for finding a maximum matching in an arbitrary graph was proposed, which has a complexity of O(n 2.5) and O(m √n?log n) where n, m are the numbers of the vertices and the edges in the graph.
Abstract: This work presents a new efficient algorithm for finding a maximum matching in an arbitrary graph. Two implementations are suggested, the complexity of the first is O(n2.5) and the complexity of the second is O(m√n?log n) where n, m are the numbers of the vertices and the edges in the graph.
313 citations
TL;DR: For a fixed pair of integers r, s ≥ 2, all positive integers m and n are determined which have the property that if the edges of Km,n (a complete bipartite graph with parts n and m) are colored with two colors, then there will always exist a path with r vertices in the first color or a path having s vertice in the second color.
56 citations
TL;DR: In this article, the minimum number of edges and vertices in a graph with edge connectivity n and exactly m n-bonds cuts was studied, and the problem was shown to be NP-hard.
Abstract: The problem studied is the following: What is the minimum number of edges and vertices in a graph with edge connectivity n and exactly m n-bonds cuts? It is perhaps surprising that this problem tur...
41 citations
24 citations
TL;DR: In this article, the authors characterized a finite friendship graph, which consists of n edge disjoint triangles such that all n>1 triangles have one vertex in common (F1 is a triangle i.e. the complete graph with three vertices).
Abstract: Abstract A friendship graph is a graph in which every two distinct vertices have exactly one common adjacent vertex (called a neighbour). Finite friendship graphs have been characterized by Erdós, Rényi and Sós [2]: Each finite friendship graph Fn which consists of n edge disjoint triangles such that all n>1 triangles have one vertex in common (F1 is a triangle i.e. the complete graph with three vertices). Thus Fn has 2n+1 vertices, 2n of them being of degree two and the remaining one (the common vertex of n triangles if n>1) being of degree 2n.
5 citations
TL;DR: Proofs are given of theorems of Lovasz and Brualdi on the existence in a finite simple graph of matchings required to meet vertices in a given set A of vertices.
4 citations