The maximal clique and colourability of curve contact graphs
نویسندگان
چکیده
منابع مشابه
The Maximal Clique and Colourability of Curve Contact Graphs
Contact graphs are a special kind of intersection graphs of geometrical objects in which the objects are not allowed to cross but only to touch each other. Contact graphs of simple curves, and line segments as a special case, in the plane are considered. The curve contact representations are studied with respect to the maximal clique and the chromatic number of the represented graphs. All possi...
متن کاملClasses and Recognition of Curve Contact Graphs,
Contact graphs are a special kind of intersection graphs of geometrical objects in which the objects are not allowed to cross but only to touch each other. Contact graphs of simple curves, and line segments as a special case, in the plane are considered. Various classes of contact graphs are introduced and the inclusions between them are described, also the recognition of the contact graphs is ...
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Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...
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An old problem on random graphs remaining open to this day is that of the existence and determination of a k-colourability threshold, already posed in the paper [10] which launched the whole subject. Using the uniformly distributed model G (n,m) of graphs with m edges on n vertices, it reads: does there exist a constant ck such that if m ∼ (ck − ε)n for some ε > 0 as n → ∞, then almost all grap...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(97)00075-9