An algorithm for identifying cycle-plus-triangles graphs

Independence Number of 2-Factor-Plus-Triangles Graphs

A 2-factor-plus-triangles graph is the union of two 2-regular graphs G1 and G2 with the same vertices, such that G2 consists of disjoint triangles. Let G be the family of such graphs. These include the famous “cycle-plus-triangles” graphs shown to be 3-choosable by Fleischner and Stiebitz. The independence ratio of a graph in G may be less than 1/3; but achieving the minimum value 1/4 requires ...

Turán numbers of bipartite graphs plus an odd cycle

Article history: Received 12 October 2012 Available online 14 February 2014

An Õ(mn) Algorithm for Minimum Cycle Basis of Graphs∗

We consider the problem of computing a minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices. In this problem, a {0, 1} incidence vector is associated with each cycle and the vector space over F2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis whe...

Extremal Graphs for Intersecting Triangles

It is known that for a graph on n vertices bn2/4c + 1 edges is sufficient for the existence of many triangles. In this paper, we determine the minimum number of edges sufficient for the existence of k triangles intersecting in exactly one common vertex. 1 Notation With integers n ≥ p ≥ 1, we let Tn,p denote the Turán graph, i.e., the complete p-partite graph on n vertices where each partite set...

Triangles in random graphs