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On the Extension of Bipartite to Parity Graphs
 Discrete Appl. Math
, 1999
"... Parity graphs form a superclass of bipartite and distancehereditary graphs. Since their introduction, all the algorithms proposed as solutions to the recognition problem and other combinatorial problems exploit the structural property of these graphs described by Burlet and Uhry in [8]. This paper ..."
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Cited by 10 (0 self)
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Parity graphs form a superclass of bipartite and distancehereditary graphs. Since their introduction, all the algorithms proposed as solutions to the recognition problem and other combinatorial problems exploit the structural property of these graphs described by Burlet and Uhry in [8]. This paper
ON PLANAR QUASIPARITY GRAPHS
, 2008
"... A graph G is strict quasi parity (SQP) if every induced subgraph of G that is not a clique contains a pair of vertices with no odd chordless path between them (an even pair). Hougardy conjectured that the minimal forbidden subgraphs for the class of SQP graphs are the odd chordless cycles, the com ..."
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Cited by 1 (1 self)
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A graph G is strict quasi parity (SQP) if every induced subgraph of G that is not a clique contains a pair of vertices with no odd chordless path between them (an even pair). Hougardy conjectured that the minimal forbidden subgraphs for the class of SQP graphs are the odd chordless cycles
A characterisation of cubic parity graphs
, 2002
"... A graph is Zmwellcovered if all maximal independent sets have the same cardinality modulo m. Zmwellcovered graphs generalise wellcovered graphs, those in which all independent sets have the same cardinality. Z2wellcovered graphs are also called parity graphs. A characterisation of cubic well ..."
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A graph is Zmwellcovered if all maximal independent sets have the same cardinality modulo m. Zmwellcovered graphs generalise wellcovered graphs, those in which all independent sets have the same cardinality. Z2wellcovered graphs are also called parity graphs. A characterisation of cubic
Recognizing Planar Strict QuasiParity Graphs
 GRAPHS AND COMBINATORICS
, 2001
"... A graph is a strictquasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an "even pair"). We presentan O(n³) algorithm for recognizing planar strict quasiparity graphs, based on WenLian Hsu's dec ..."
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Cited by 4 (2 self)
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A graph is a strictquasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an "even pair"). We presentan O(n³) algorithm for recognizing planar strict quasiparity graphs, based on WenLian Hsu
Uniquely Hamiltonian Characterizations of DistanceHereditary and Parity Graphs
"... A graph is shown to be distancehereditary if and only if no induced subgraph of order five or more has a unique hamiltonian cycle; this is also equivalent to every induced subgraph of order five or more having an even number of hamiltonian cycles. Restricting the induced subgraphs to those of odd o ..."
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order five or more gives two similar characterizations of parity graphs. The close relationship between distancehereditary and parity graphs is unsurprising, but their connection with hamiltonian cycles of induced subgraphs is unexpected. 1 Distancehereditary graphs Howorka [10] defined a graph to be a
Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition
 JOURNAL OF ALGORITHMS
, 1998
"... We present efficient (parallel) algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solve some algorithmic problems in graphs. This includes split decomposition. We show that efficient parallel split decomposition induces an efficient para ..."
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Cited by 39 (1 self)
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parallel parity graph recognition algorithm. This is a consequence of the result of [7] that parity graphs are exactly those graphs that can be split decomposed into cliques and bipartite graphs.
A Characterization for Parity Graphs and a Coloring Problem With Costs
, 1998
"... In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that G is a parity graph, if and only if the cartesian product G K 2 is a perfect graph. Furthermore, as a ..."
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Cited by 1 (0 self)
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In this paper, we give a characterization for parity graphs. A graph is a parity graph, if and only if for every pair of vertices all minimal chains joining them have the same parity. We prove that G is a parity graph, if and only if the cartesian product G K 2 is a perfect graph. Furthermore, as a
Design of capacityapproaching irregular lowdensity paritycheck codes
 IEEE TRANS. INFORM. THEORY
, 2001
"... We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the unde ..."
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Cited by 581 (6 self)
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We design lowdensity paritycheck (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming
The MerriVeldSimmons conjecture also holds for parity graphs
"... The MerriVeldSimmons conjectures states a relation between the distance of vertices in a simple graph G and the number of independent sets, denoted as σ(G), in vertexdeleted subgraphs. Namely, that the sign of the term σ(G−u) · σ(G−v) − σ(G) · σ(G−u−v) only depends on the parity of the distanc ..."
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The MerriVeldSimmons conjectures states a relation between the distance of vertices in a simple graph G and the number of independent sets, denoted as σ(G), in vertexdeleted subgraphs. Namely, that the sign of the term σ(G−u) · σ(G−v) − σ(G) · σ(G−u−v) only depends on the parity
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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