Truss decomposition using triangle graphs

Gallai's path decomposition conjecture for triangle-free planar graphs

A path decomposition of a graph G is a collection of edge-disjoint paths of G that covers the edge set of G. Gallai (1968) conjectured that every connected graph on n vertices admits a path decomposition of cardinality at most ⌊(n + 1)/2⌋. Gallai’s Conjecture has been verified for many classes of graphs. In particular, Lovász (1968) verified this conjecture for graphs with at most one vertex wi...

Truss Decomposition in Massive Networks

The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core which is also efficient to compute, k-truss represents the “core” of a k-core that keeps the key information of, while filtering out less important informat...

Triangle Graphs

We introduce a new class of planar graphs called triangle graphs. First, we present a formal way of constructing and characterizing triangle graphs, and then show that they characterize the adjacencies of arbitrary triangulations and they are three-colorable for a certain subclass of triangulations. Subsequently, we discuss an application of triangle graphs to the parallel nite element solution...

Drawing graphs using modular decomposition

Abstract. In this paper we present an algorithm for drawing an undirected graph G which takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by traversing the modular decomposition tree of the input graph G on n vertices and m edges, in a bottom-up fashion until it reaches the root of the tree, while at the same time intermediate drawings ar...

Measuring triangle-free graphs