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Strengthening strongly chordal graphs
Discrete Mathematics, Algorithms and Applications, 2016An [Formula: see text]-chord of a cycle [Formula: see text] is a chord that forms a new cycle with a length-[Formula: see text] subpath of [Formula: see text] when [Formula: see text] is at most half the length of [Formula: see text]. Define a graph to be [Formula: see text]-strongly chordal if, for every [Formula: see text], every cycle long enough ...
T. McKee
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Roman domination on strongly chordal graphs
Journal of Combinatorial Optimization, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chun-Hung Liu, G. Chang
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Characterizing Strongly Chordal Graphs by Using Minimal Relative Separators
Combinatorial Designs and Applications, 2020Shaohan Ma, Julin Wu
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Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs
International Colloquium on Automata, Languages and Programming, 2002Chordal bipartite graphs are introduced to analyze nonsymmetric matrices, and form a large class of perfect graphs. There are several problems, which can be solved efficiently on the class using the characterization by the doubly lexical ordering ofthe bipartite adjacency matrix.
Ryuhei Uehara
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Steiner trees, connected domination and strongly chordal graphs
Networks, 1985AbstractWe consider Steiner tree problems and connected dominating set problems for several classes of graphs. We give a polynomial algorithm and a min‐max theorem for the cardinality Steiner problem in strongly chordal graphs and a polynomial algorithm for the weighted connected dominating set problem in series‐parallel graphs.
K. White, M. Farber, W. Pulleyblank
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Complexity Analysis of Triangular Decomposition over F_2 with Strongly Chordal Graphs
International Symposium on Symbolic and Algebraic ComputationIn this paper, we first introduce a new vertex order of graphs called the substrong elimination ordering based on maximal cliques of the graphs and prove that such an ordering can fully characterize strongly chordal graphs.
Zhaoxing Qi, Chenqi Mou
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Strong clique trees, neighborhood trees, and strongly chordal graphs
Journal of Graph Theory, 2000A graph is a strongly chordal graph, if it is chordal and every cycle of even length at least six has a chord that divides the cycle into two odd-length paths. Whereas maximal complete subgraphs and clique trees are central objects in the theory of chordal grahps, a simple notion of strong clique trees allows to extend this structure to strongly ...
T. McKee
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On Generating Strong Elimination Orderings of Strongly Chordal Graphs
Foundations of Software Technology and Theoretical Computer Science, 1998We present a conceptually simple algorithm to generate an ordering of the vertices of an undirected graph. The ordering generated turns out to be a strong elimination ordering if and only if the given graph is a strongly chordal graph. This algorithm makes use of maximum cardinality search and lexicographic breadth first search algorithms which are ...
N. K. R. Prasad, P. S. Kumar
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Partitioning Cliques of Claw-Free Strongly Chordal Graphs
1999In this paper we find a particular partition of the vertex set of claw-free strongly chordal graphs in which each element is a clique, and we show that the adjacency graph of these cliques is a tree. In particular, the presented results imply the existence of an ordering of the vertices, and a corresponding edge orientation, such that each directed ...
Confessore, G +2 more
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SIAM Journal on Computing, 1999
Summary: We study the parameterized complexity of three NP-hard graph completion problems. The minimum fill-in problem asks if a graph can be triangulated by adding at most \(k\) edges. We develop \(O(c^k m)\) and \(O(k^2 mn+f(k))\) algorithms for this problem on a graph with \(n\) vertices and \(m\) edges. Here \(f(k)\) is exponential in \(k\) and the
Kaplan, Haim +2 more
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Summary: We study the parameterized complexity of three NP-hard graph completion problems. The minimum fill-in problem asks if a graph can be triangulated by adding at most \(k\) edges. We develop \(O(c^k m)\) and \(O(k^2 mn+f(k))\) algorithms for this problem on a graph with \(n\) vertices and \(m\) edges. Here \(f(k)\) is exponential in \(k\) and the
Kaplan, Haim +2 more
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