In this work we investigate the complexity of some problems related to the Simultaneous Embedding with Fixed Edges (SEFE) of k planar graphs and the PARTITIONED k-PAGE BOOK EMBEDDING (PBE-k) problems, which are known to be equivalent under certain conditions. While the computational complexity of SEFE for k = 2 is still a central open question in Graph Drawing, the problem is NP-complete for k ...

Outerstring graphs are the intersection graphs of curves that lie inside a disk such that each curve intersects the boundary of the disk in one of its endpoints. Outerstring graphs were introduced in 1991 and are amongst the most general classes of intersection graphs studied, including among others, chordal graphs and interval filament graphs. To date no polynomial time algorithm is known for ...

A graph G with vertex set V is said to be n-existentially closed if, for every S ⊂ V with |S| = n and every T ⊆ S, there exists a vertex x ∈ V − S such that x is adjacent to each vertex of T but is adjacent to no vertex of S − T . Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and...

We prove that every planar graph is an intersection graph of strings in the plane such that any two strings intersect at most once.

Chang, Y.-W., M.S. Jacobson, CL. Monma and D.B. West, Subtree and substar intersection numbers. Discrete Applied Mathematics 44 (1993) 205-220. We introduce the star number [free number] of a graph, being the minimum t such that G is the intersection graph of unions of t substars [subtrees] of a host tree. We study bounds on these parameters, compare them with interval number, and characterize ...

We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k–connectivity, perfect matching containment and Hamilton cycle containment. keywords: random intersection graph, threshold functions, connectivity, Hamilton cycle, perfect ...

Block-intersection graphs of Steiner triple systems are considered. We prove that the block-intersection graphs of non-isomorphic Steiner triple systems are themselves non-isomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable block-intersection graph.

T. Tamizh Chelvam and T. Asir [15] studied the intersection graph of gamma sets in the total graph of a commutative Artin ring. The intersection graph ITΓ(R) of gamma sets in the total graph of a commutative ring R, is the undirected graph with vertex as collection of all γ-sets in the total graph of R and two distinct vertices u and v are adjacent if and only if u ∩ v 6= ∅. In this paper, we c...

We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time O(n). We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an O(n tw(G) ) time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid g...

A function diagram (f-diagram) D consists of the family of curves {i, . . . , ii} obtained from n continuous functions fi : [O, 1] -B R (1 G i d n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement 0 is a comparability graph. An f-diagram generalizes the notion cf a permutation diagram where the fi are linear ...