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Bipartite Dimensions And Bipartite Degrees Of Graphs
 DISCRETE MATH
, 1993
"... A cover (bipartite) of a graph G is a family of complete bipartite subgraphs of G whose edges cover G's edges. G's bipartite dimension d(G) is the minimum cardinality of a cover, and its bipartite degree j(G) is the minimum over all covers of the maximum number of covering members incident ..."
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A cover (bipartite) of a graph G is a family of complete bipartite subgraphs of G whose edges cover G's edges. G's bipartite dimension d(G) is the minimum cardinality of a cover, and its bipartite degree j(G) is the minimum over all covers of the maximum number of covering members
Bipartite rigidity
"... We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs, and define for two positive integers k, l the notions of (k, l)rigid and (k, l)stress free bipartite graphs. This theory coincides with the study of Babson–Novik’s balanced sh ..."
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We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs, and define for two positive integers k, l the notions of (k, l)rigid and (k, l)stress free bipartite graphs. This theory coincides with the study of Babson–Novik’s balanced
RESOLUTION OF UNMIXED BIPARTITE GRAPHS
, 2009
"... A For an unmixed bipartite graph G we consider the lattice of vertex covers LG and compute depth, projective dimension and extremal Bettinumbers of R/I(G) in terms of this lattice. ..."
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A For an unmixed bipartite graph G we consider the lattice of vertex covers LG and compute depth, projective dimension and extremal Bettinumbers of R/I(G) in terms of this lattice.
On the First Eigenvalue of Bipartite Graphs
"... In this paper we study the maximum value of the largest eigenvalue for simple bipartite graphs, where the number of edges is given and the number of vertices on each side of the bipartition is given. We state a conjectured solution, which is an analog of the BrualdiHoffman conjecture for general gr ..."
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graphs, and prove the conjecture in some special cases. Key words. Bipartite graph, maximal eigenvalue, BrualdiHoffman conjecture, degree, sequences, chain graphs. 1
On the Cubicity of Bipartite Graphs
, 2008
"... A unit cube in kdimension (or a kcube) is defined as the cartesian product R1×R2× · · ·×Rk, where each Ri is a closed interval on the real line of the form [ai, ai + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of kcubes. Many N ..."
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A unit cube in kdimension (or a kcube) is defined as the cartesian product R1×R2× · · ·×Rk, where each Ri is a closed interval on the real line of the form [ai, ai + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of kcubes. Many
Dominance Drawings of Bipartite Graphs
, 1994
"... Let G = (S; T; E) denote a directed bipartite graph with S a set of sources and T a set of sinks. Using vectors s = (s1 ; s2 ; :::s k) and t = (t1 ; t2 ; :::t k) in R k to represent the elements s 2 S and t 2 T we can geometrically characterize the properties of G. We consider the case where s ..."
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Let G = (S; T; E) denote a directed bipartite graph with S a set of sources and T a set of sinks. Using vectors s = (s1 ; s2 ; :::s k) and t = (t1 ; t2 ; :::t k) in R k to represent the elements s 2 S and t 2 T we can geometrically characterize the properties of G. We consider the case where
On the Dominator Colorings in Bipartite Graphs
"... A graph has a dominator coloring if it has a proper coloring in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number χd(G) is the minimum number of color classes in a dominator coloring of a graph G. In this paper we study the dominator chromati ..."
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chromatic number for the hypercube, Qn = Qn−1 × K2 (with Q1 ∼ = P2, n ≥ 2), and more generally for bipartite graphs. We then conclude it with open questions for further research. 1
Local Minima in the Graph Bipartitioning Problem
, 1996
"... We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an explanation in terms of the correlation length of its landscape. ..."
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Cited by 9 (5 self)
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We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an explanation in terms of the correlation length of its landscape.
SHELLABLE GRAPHS AND SEQUENTIALLY COHENMACAULAY BIPARTITE GRAPHS
, 2007
"... Associated to a simple undirected graph G is a simplicial complex ∆G whose faces correspond to the independent sets of G. We call a graph G shellable if ∆G is a shellable simplicial complex in the nonpure sense of BjörnerWachs. We are then interested in determining what families of graphs have t ..."
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Cited by 35 (7 self)
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the property that G is shellable. We show that all chordal graphs are shellable. Furthermore, we classify all the shellable bipartite graphs; they are precisely the sequentially CohenMacaulay bipartite graphs. We also give an inductive procedure to build all such shellable bipartite graphs. Because shellable
Results 1  10
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19,484