Results 71 to 80 of about 552 (213)
The Hadwiger number, chordal graphs and -perfection
AKCE International Journal of Graphs and Combinatorics, 2017 A graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms of the Hadwiger number and we also characterize the families of graphs ...
Christian Rubio-Montiel
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Clique roots of K4-free chordal graphs
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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On b-perfect Chordal Graphs [PDF]
Graphs and Combinatorics, 2009 The b-chromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the b-chromatic number is equal to the chromatic number for every induced subgraph.
Maffray, Frédéric, Mechebbek, Meriem
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Stable Cuts, NAC‐Colourings and Flexible Realisations of Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A (2‐dimensional) realisation of a graph G $G$ is a pair ( G , p ) $(G,p)$, where p $p$ maps the vertices of G $G$ to R 2 ${{\mathbb{R}}}^{2}$. A realisation is flexible if it can be continuously deformed while keeping the edge lengths fixed, and rigid otherwise.
Katie Clinch +5 more
wiley +1 more source
Discrete Mathematics, 2003 This paper studies dual-chordal graphs, that is, graphs that are dual to chordal graphs with regard to cycle/cutset duality. A characteristic of such graphs is that every cutset with at least four edges is accompanied by a certain kind of edge, a ``cut-chord.'' One result allows us to recognize dual-chordal graphs by simply looking at cubic graphs.
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Weak Degeneracy of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The weak degeneracy of a graph G $G$ is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every d $d$‐degenerate graph is weakly d $d$‐degenerate, but the converse is not true in general (e.g., all connected d $d$‐regular graphs except ...
Anton Bernshteyn +2 more
wiley +1 more source
Discrete Applied Mathematics, 2002 A chordally signed graph is defined as a signed chordal graph (each edge is designated as being positive or negative and every induced cycle is a triangle) in which every cycle \(C\) containing an even number of negative edges (positive cycles) has a chord \(e\) such that \(C\cup\{e\}\) forms two positive cycles.
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A Min–Max Relation on Dicuts and Dijoins in Weighted Chordal Digraphs
Journal of Graph Theory, EarlyView.ABSTRACT In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects every dicut. Edmonds and Giles conjectured that in a weighted digraph, the minimum weight of a dicut is equal to the maximum size of a packing of dijoins. This has been disproved. However, the unweighted version conjectured by
Gérard Cornuéjols, Siyue Liu, R. Ravi
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Chordal Completions of Planar Graphs
Journal of Combinatorial Theory, Series B, 1994 A graph is chordal if there are no induced cycles of length 4 or more. A chordal completion of a graph is formed by adding edges until the resulting graph is chordal. What is the minimal number of edges in a chordal completion? The authors answer this question for the class of planar graphs: every planar graph on \(n\) vertices has a chordal completion
Fan R. K. Chung, David Mumford
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Explicit 3‐colorings for Exponential Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +2 more
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