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Nowherezero Unoriented Flows in Hamiltonian Graphs
"... An unoriented flow in a graph, is an assignment of real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. This is equivalent to a flow in a bidirected graph all of whose edges are extraverted. A nowherezero unoriented kflow is an unoriented flow ..."
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with values from the set {±1,...,±(k − 1)}. It has been conjectured that if a graph has a nowherezero unoriented flow, then it admits a nowherezero unoriented 6flow. We prove that this conjecture is true for hamiltonian graphs, with 6 replaced by 12. ∗Keywords: Hamiltonian graph, nowherezero flow
NowhereZero kFlows on Graphs
, 2012
"... A flow on an oriented graph Γ is a labeling of edges from a group such that the sum of the values flowing into each node is equal to the sum of values flowing out of each node. When the group is Zk or Z (with the labels bounded by k in absolute value), there is an established theory of counting nowh ..."
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nowherezero flows, i.e., the flows where no edge gets labeled 0. This theory includes results about polynomiality of the flowcounting function and combinatorial reciprocity theorems. We introduce nowherezero kflows, where each edge has a different range of allowable values, and propose an analogous
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Duality, NowhereZero Flows, Colorings and Cycle Covers
, 1999
"... NowhereZero Flows Problems, Coloring problems, Cycle cover problems lie in the core of graph theory. The strong relationship between them is the duality. Several important (and beautiful) conjectures are still open and this a very active field of study. We presente this subject with the enlightenin ..."
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NowhereZero Flows Problems, Coloring problems, Cycle cover problems lie in the core of graph theory. The strong relationship between them is the duality. Several important (and beautiful) conjectures are still open and this a very active field of study. We presente this subject
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Algebraic Methods for Reducibility in NowhereZero Flows
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii We study reducibility for nowherezero flows. A reduci ..."
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reducibility proof typically consists of showing that some induced subgraphs cannot appear in a minimum counterexample to some conjecture. We derive algebraic proofs of reducibility. We define variables which in some sense count the number of nowherezero flows of certain type in a graph and then deduce
NowhereZero Flows in Random Graphs
"... A nowherezero 3ow in a graph G is an assignment of a direction and a value 1 or 2 to each edge of G such that for each vertex v in G, the sum of the values of the edges with tail v equals the sum of the values of the edges with head v. Motivated by results about regioncoloring of planar graphs ..."
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Cited by 1 (0 self)
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A nowherezero 3ow in a graph G is an assignment of a direction and a value 1 or 2 to each edge of G such that for each vertex v in G, the sum of the values of the edges with tail v equals the sum of the values of the edges with head v. Motivated by results about regioncoloring of planar
Results 1  10
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29,243