Characterizing intersection classes of graphs
نویسندگان
چکیده
منابع مشابه
On cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
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We analyse properties of geometric intersection graphs to show strict containment between some natural classes of geometric intersection graphs. In particular, we show the following properties: • A graph G is outerplanar if and only if the 1-subdivision of G is outer-segment. • For each integer k > 1, the class of intersection graphs of segments with k different lengths is a strict subclass of ...
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A general method for the computation of various parameters measuring the vulnerability of a graph is introduced. Four measures of vulnerability are considered, i.e., the toughness, scattering number, vertex integrity and the size of a minimum balanced separator. We show how to compute these parameters by polynomial time algorithms for various classes of intersection graphs like permutation grap...
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We show that the class of unit grid intersection graphs properly includes both of the classes of interval bigraphs and of P6-free chordal bipartite graphs. We also demonstrate that the classes of unit grid intersection graphs and of chordal bipartite graphs are incomparable. © 2007 Elsevier B.V. All rights reserved.
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The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1985
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90047-0