Intersection Graphs of Segments
نویسندگان
چکیده
منابع مشابه
Intersection Graphs of Rays and Grounded Segments
We consider several classes of intersection graphs of line segments in the plane and prove new equality and separation results between those classes. In particular, we show that: • intersection graphs of grounded segments and intersection graphs of downward rays form the same graph class, • not every intersection graph of rays is an intersection graph of downward rays, and • not every intersect...
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An L-shape is the union of a horizontal and a vertical segment with a common endpoint. These come in four rotations: L, L , Land L . A k-bend path is a simple path in the plane, whose direction changes k times from horizontal to vertical. If a graph admits an intersection representation in which every vertex is represented by an L, an L or L , a k-bend path, or a segment, then this graph is cal...
متن کاملIntersection graphs of segments and $\exists\mathbb{R}$
A graph G with vertex set {v1, v2, . . . , vn} is an intersection graph of segments if there are segments s1, . . . , sn in the plane such that si and sj have a common point if and only if {vi, vj} is an edge of G. In this expository paper, we consider the algorithmic problem of testing whether a given abstract graph is an intersection graph of segments. It turned out that this problem is compl...
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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. ...
متن کاملIntersection graphs associated with semigroup acts
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: Journal of Combinatorial Theory, Series B
سال: 1994
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1071