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Tuza's Conjecture for graphs with maximum average degree less than 7
TLDR
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
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Codes for DNA Sequence Profiles
TLDR
We consider the problem of storing and retrieving information from synthetic DNA media. Expand
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Correlation Clustering and Biclustering With Locally Bounded Errors
TLDR
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
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Motif clustering and overlapping clustering for social network analysis
TLDR
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
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Correlation Clustering with Constrained Cluster Sizes and Extended Weights Bounds
TLDR
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
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Paired threshold graphs
TLDR
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
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On a Conjecture of Erdős, Gallai, and Tuza
TLDR
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
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Complexity of a disjoint matching problem on bipartite graphs
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 $M_2$ saturatesExpand
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Maximal k-edge-colorable subgraphs, Vizing's Theorem, and Tuza's Conjecture
TLDR
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
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Extremal aspects of the Erdős-Gallai-Tuza conjecture
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
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