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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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graphs Tutte conjectured in 1966 that every 4edgeconnected graph has a nowherezero 3ow. This remains open. In this paper we study nowherezero ows in random graphs and prove that almost surely as soon as the random graph G(n; p) has minimum degree two it has a nowherezero 3ow. This result
The number of nowherezero flows in graphs and signed graphs
 J. Combin. Theory Ser. B
, 2006
"... Abstract. The existence of an integral flow polynomial that counts nowherezero kflows on a graph, due to Kochol, is a consequence of a general theory of insideout polytopes. The same holds for flows on signed graphs. We develop these theories, as well as the related counting theory of nowherezer ..."
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Cited by 16 (6 self)
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Abstract. The existence of an integral flow polynomial that counts nowherezero kflows on a graph, due to Kochol, is a consequence of a general theory of insideout polytopes. The same holds for flows on signed graphs. We develop these theories, as well as the related counting theory of nowherezero
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
Nowherezero 3flows in Cayley graphs of Abelian groups
, 2002
"... We characterize Cayley graphs of abelian groups which admit a nowherezero 3flow. In particular, we prove that every kvalent Cayley graph of an abelian group, where k ≥ 4, admits a nowherezero 3flow. ..."
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We characterize Cayley graphs of abelian groups which admit a nowherezero 3flow. In particular, we prove that every kvalent Cayley graph of an abelian group, where k ≥ 4, admits a nowherezero 3flow.
Extending a Partial NowhereZero 4Flow
, 1999
"... ... every graph with 2 edgedisjoint spanning trees admits a nowherezero 4flow. In [J Combin Theory Ser B, 56 (1992), 165–182], Jaeger et al. extended this result by showing that, if A is an abelian group with A  =4, then every graph with 2 edgedisjoint spanning trees is Aconnected. As graphs ..."
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... every graph with 2 edgedisjoint spanning trees admits a nowherezero 4flow. In [J Combin Theory Ser B, 56 (1992), 165–182], Jaeger et al. extended this result by showing that, if A is an abelian group with A  =4, then every graph with 2 edgedisjoint spanning trees is Aconnected. As graphs
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 ..."
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
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
Results 1  10
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1,842,510