Tuza's Conjecture states that if a graph G does not contain more than k edge-disjoint triangles, then some set of at most 2 k edges meets all triangles of G .Expand

We introduce a new framework that allows the objective to be a more general function of the number of errors at each vertex and provides a rounding algorithm which converts “fractional clusterings” into discrete clusterings while causing only a constant-factor blowup.Expand

We introduce a new clustering paradigm termed motif clustering that aims to minimize the number of clustering errors associated with both edges and certain higher order graph structures (motifs) that represent “atomic units” of social organizations.Expand

We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges.Expand

We introduce a new class of graphs termed Paired Threshold (PT) graphs described through vertex weights that govern the existence of edges via two inequalities.Expand

Erdős, Gallai, and Tuza posed the following problem: given an n-vertex graph G, let i¾?1G denote the smallest size of a set of edges whose deletion makes G triangle-free, and let α1G denotes the largest size of edges containing at most one edge from each triangle of G.Expand

We consider the following question: given an $(X,Y)$-bigraph $G$ and a set $S \subset X$, does $G$ contain two disjoint matchings $M_1$ and $M_2$ such that $M_1$ saturates $X$ and $M_2$ saturates… Expand

We prove that if M is a maximal k-edge-colorable subgraph of a multigraph G and if F={vV(G):dM(v)k(v), then dF(v)= dM (v) for all vV(V) with dM(V).Expand

Erd?s, Gallai, and Tuza posed the following problem: given an n -vertex graph G , let ? 1 ( G ) denote the smallest size of a set of edges whose deletion makes G triangle-free, and let α 1 ( G )… Expand