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The Neighborhood Polynomial of Chordal Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor.
Helena Bergold +2 more
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Edge erasures and chordal graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph.
Jared Culbertson +2 more
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The leafage of a chordal graph [PDF]
Discussiones Mathematicae Graph Theory, 1998 The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes.
Lin, In-Jen +2 more
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Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs [PDF]
Logical Methods in Computer Science, 2019 We show that the class of chordal claw-free graphs admits LREC$_=$-definable canonization. LREC$_=$ is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion.
Berit Grußien
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Discrete Mathematics & Theoretical Computer Science, 2019 Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph $G=(V,E)$, a geodesic triangle $\bigtriangleup(x,y,z)$ with $x, y, z\in V$ is the union $P(x,y) \cup P(x,z) \cup P(y,z)$ of three shortest paths connecting ...
Feodor F. Dragan, Abdulhakeem Mohammed
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Learning Continuous Decomposable Models Using Mutual Information and Statistical Copulas [PDF]
EntropyLearning dependence graphs from multivariate continuous data is challenging when marginal distributions are heterogeneous, since likelihood-based nonparametric scores can be sensitive to smoothing choices and can confound marginal irregularities ...
Luiz Desuó Neto +3 more
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Recognition of chordal graphs and cographs which are Cover-Incomparability graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceCover-Incomparability graphs (C-I graphs) are an interesting class of graphs from posets. A C-I graph is a graph from a poset $P=(V,\le)$ with vertex set $V$, and the edge-set is the union of edge sets of the cover graph and the incomparability graph of ...
Arun Anil, Manoj Changat
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Chordal Graphs are Fully Orientable [PDF]
, 2012 Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let m and M denote the minimum and the maximum of the number of dependent arcs over all acyclic orientations of G.
Lai, Hsin-Hao, Lih, Ko-Wei
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Clique roots of K4-free chordal graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2019 The clique polynomial C(G, x) of a finite, simple and undirected graph G = (V, E) is defined as the ordinary generating function of the number of complete subgraphs of G. A real root of C(G, x) is called a clique root of the graph G.
Hossein Teimoori Faal
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Parameterized complexity and inapproximability of dominating set problem in chordal and near chordal graphs [PDF]
Journal of Combinatorial Optimization, 2010 Yinglei Song
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