On the interval number of random graphs

On the Independen e Number of Random Interval Graphs

On The Independence Number Of Random Interval Graphs

A random interval graph of order n is generated by picking 2n numbers X 1 : : : X 2n independently from the uniform distribution on 0; 1] and considering the collection of n intervals with extremities X 2i?1 and X 2i for i 2 f1;:::ng. The graph vertices correspond to intervals. Two vertices are connected if the corresponding intervals intersect. This paper characterizes the uctuations of the in...

On the interval number of special graphs

The interval number of a graph G is the least natural number t such that G is the intersection graph of sets, each of which is the union of at most t intervals, denoted by i (G ). Griggs and West showed that i(G) d12(d þ 1)e. We describe the extremal graphs for that inequality when d is even. For three special perfect graph classes we give bounds on the interval number in terms of the independe...

On the fixed number of graphs

‎A set of vertices $S$ of a graph $G$ is called a fixing set of $G$‎, ‎if only the trivial automorphism of $G$ fixes every vertex in $S$‎. ‎The fixing number of a graph is the smallest cardinality of a fixing‎ ‎set‎. ‎The fixed number of a graph $G$ is the minimum $k$‎, ‎such that ‎every $k$-set of vertices of $G$ is a fixing set of $G$‎. ‎A graph $G$‎ ‎is called a $k$-fixed graph‎, ‎if its fix...

On the saturation number of graphs

Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...