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Algorithms for Generating Strongly Chordal Graphs
Lecture Notes in Computer Science, 2021Graph generation serves many useful purposes: cataloguing, testing conjectures, to which we would like to add that of producing test instances for graph algorithms. Strongly chordal graphs are a subclass of chordal graphs for which polynomial-time algorithms could be designed for problems which are NP-complete for the parent class of chordal graphs. In
Asish Mukhopadhyay, Mukhopadhyay Asish
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Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs
Lecture Notes in Computer Science, 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, Uehara Ryuhei
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A linear-time algorithm for semitotal domination in strongly chordal graphs
Discrete Applied Mathematics, 2021 In a graph $G=(V,E)$ with no isolated vertex, a dominating set $D \subseteq V$, is called a semitotal dominating set if for every vertex $u \in D$ there is another vertex $v \in D$, such that distance between $u$ and $v$ is at most two in $G$.
Vikash Tripathi +2 more
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Odd twists on strongly chordal graphs
Discrete Mathematics, Algorithms and Applications, 2019Strongly chordal graphs can be characterized as chordal graphs in which every even cycle of length at least [Formula: see text] has an odd chord (a chord whose endpoints are an odd distance apart in the cycle subgraph).
T. McKee
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Strongly chordal graphs as intersection graphs of trees (Farber's proof revisited)
CoRRIn his Ph.D. thesis, Farber proved that every strongly chordal graph can be represented as intersection graph of subtrees of a weighted tree, and these subtrees are ``compatible''.
Therese Biedl
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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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Characterizing s-strongly chordal bipartite graphs
Utilitas MathematicaThe strongly chordal graph literature has recently expanded to include the sequentially smaller classes of \(s\)-strongly chordal graphs for \(s = 1, 2, 3,\ldots\) (and the limiting class of majorly chordal graphs).
T. McKee
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