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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
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
Perfect Matchings in Clawfree Cubic Graphs
, 2009
"... Lovász and Plummer conjectured that there exist a fixed positive constant c such that every cubic nvertex graph with no cutedge has at least 2 cn perfect matchings. Their conjecture has been verified for bipartite graphs by Voorhoeve and planar graphs by Chudnovsky and Seymour. We prove that every ..."
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Cited by 2 (0 self)
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clawfree cubic nvertex graph with no cutedge has more than 2 n/18 perfect matchings, thus verifying the conjecture for clawfree graphs.
NowhereZero 3Flows in Squares of Graphs
, 2003
"... It was conjectured by Tutte that every 4edgeconnected graph admits a nowherezero 3flow. In this paper, we give a complete characterization of graphs whose squares admit nowherezero 3flows and thus confirm Tutte's 3flow conjecture for the family of squares of graphs. ..."
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Cited by 4 (3 self)
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It was conjectured by Tutte that every 4edgeconnected graph admits a nowherezero 3flow. In this paper, we give a complete characterization of graphs whose squares admit nowherezero 3flows and thus confirm Tutte's 3flow conjecture for the family of squares of graphs.
Nowherezero 3flows in locally connected graphs
 J. Graph Theory
, 1999
"... Abstract: Let G be a graph. For each vertex v 2V (G), Nv denotes the subgraph induces by the vertices adjacent to v in G. The graph G is locally kedgeconnected if for each vertex v 2V (G), Nv is kedgeconnected. In this paper we study the existence of nowherezero 3flows in locally kedgeconnect ..."
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Cited by 12 (9 self)
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Abstract: Let G be a graph. For each vertex v 2V (G), Nv denotes the subgraph induces by the vertices adjacent to v in G. The graph G is locally kedgeconnected if for each vertex v 2V (G), Nv is kedgeconnected. In this paper we study the existence of nowherezero 3flows in locally k
Nowherezero 3flows in triangularly connected graphs
 JOURNAL OF COMBINATORIAL THEORY, SERIES B 98 (2008) 1325–1336
, 2008
"... Let H1 and H2 be two subgraphs of a graph G. We say that G is the 2sum of H1 and H2, denoted by H1 ⊕2 H2,ifE(H1) ∪ E(H2) = E(G), V(H1) ∩ V(H2)=2, and E(H1) ∩ E(H2)=1. A trianglepath in a graph G is a sequence of distinct triangles T1T2 ···Tm in G such that for 1 � i � m − 1, E(Ti) ∩ E(Ti+ ..."
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Cited by 8 (3 self)
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has no nowherezero 3flow if and only if there is an odd wheel W and a subgraph G1 such that G = W ⊕2 G1, where G1 is a triangularly connected graph without nowherezero 3flow. Repeatedly applying the result, we have a complete characterization of triangularly connected graphs which have no nowherezero
NowhereZero KFlows of Supergraphs
"... Let G be a 2edgeconnected graph with o vertices of odd degree. It is wellknown that one should (and can) add o 2 edges to G in order to obtain a graph which admits a nowherezero 2flow. We prove that one can add to G asetof## o 4 #, # 1 2 # o 5 ##,and # 1 2 # o 7 ## edges such t ..."
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such that the resulting graph admits a nowherezero 3flow, 4flow, and 5flow, respectively. 1
NOWHEREZERO kFLOWS OF SUPGRAPHS
, 2000
"... Let G be a 2edgeconnected graph with o vertices of odd degree. It is wellknown that one should (and can) add o 2 edges to G in order to obtain a graph which admits a nowherezero 2flow. We prove that one can add to G asetof≤⌊o 1 o 1 o 4⌋, ⌈ 2 ⌊ 5⌋⌉, and⌈2⌊7⌋ ⌉ edges such that the resulting graph ..."
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
Results 1  10
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