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Representations of Edge Intersection Graphs of Paths in a Tree [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $\mathcal{P}$ be a collection of nontrivial simple paths in a tree $T$. The edge intersection graph of $\mathcal{P}$, denoted by EPT($\mathcal{P}$), has vertex set that corresponds to the members of $\mathcal{P}$, and two vertices are joined by an ...
Martin Charles Golumbic +2 more
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The Dilworth Number of Auto-Chordal-Bipartite Graphs [PDF]
, 2013 The mirror (or bipartite complement) mir(B) of a bipartite graph B=(X,Y,E) has the same color classes X and Y as B, and two vertices x in X and y in Y are adjacent in mir(B) if and only if xy is not in E. A bipartite graph is chordal bipartite if none of
Berry, Anne +2 more
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Complexity of Hamiltonian Cycle Reconfiguration
Algorithms, 2018 The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained ...
Asahi Takaoka
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The Lefthanded Local Lemma characterizes chordal dependency graphs [PDF]
, 2012 Shearer gave a general theorem characterizing the family $\LLL$ of dependency graphs labeled with probabilities $p_v$ which have the property that for any family of events with a dependency graph from $\LLL$ (whose vertex-labels are upper bounds on the ...
Pegden, Wesley
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Maxclique and Unit Disk Characterizations of Strongly Chordal Graphs
Discussiones Mathematicae Graph Theory, 2014 Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new ...
Caria Pablo De, McKee Terry A.
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On the multipacking number of grid graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted $\gamma_b(G)$.
Laurent Beaudou, Richard C. Brewster
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Efficient generation of elimination trees and graph associahedra
ACM-SIAM Symposium on Discrete Algorithms, 2022 An elimination tree for a connected graph G is a rooted tree on the vertices of G obtained by choosing a root x and recursing on the connected components of G − x to produce the subtrees of x .
J. Cardinal +2 more
semanticscholar +1 more source
Discrete Applied Mathematics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Udi Rotics, Uri N. Peled
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Algorithms and complexity for geodetic sets on planar and chordal graphs [PDF]
International Symposium on Algorithms and Computation, 2020 We study the complexity of finding the \emph{geodetic number} on subclasses of planar graphs and chordal graphs. A set $S$ of vertices of a graph $G$ is a \emph{geodetic set} if every vertex of $G$ lies in a shortest path between some pair of vertices of
Dibyayan Chakraborty +5 more
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Chordal Editing is Fixed-Parameter Tractable [PDF]
, 2014 Graph modification problems typically ask for a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property ...
A Hajnal +19 more
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