In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.

A conjecture of M\'a\u{c}ajov\'a and \u{S}koviera asserts that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.

The intersection graph of a collection of sets F is the graph obtained by assigning a distinct vertex to each set in F and joining two vertices by an edge precisely when their corresponding sets have a nonempty intersection. When F is allowed to be an arbitrary family of sets, the class of graphs obtained as intersection graphs is simply all undirected graphs. When the types of sets allowed in ...

To a rhombic embedding of a planar graph with quadrilateral faces and vertices colored black and white there is an associated isoradial circle pattern C 1 with centers of circles at white vertices and radii equal to the edge length. Let C 2 be another circle pattern such that the rhombi correspond to kites of intersecting circles with the same intersection angles. We consider the mapping g C wh...

A conjecture of Kaiser and Raspaud [6] asserts (in a special form due to Má cajová and Skoviera) that every bridgeless cubic graph has two perfect matchings whose intersection does not contain any odd edge cut. We prove this conjecture for graphs with few vertices and we give a stronger result for traceable graphs.

In this contribution, we are concerned with the detection and re ned localization of 3D point landmarks. We propose multi-step di erential procedures for subvoxel localization of 3D point landmarks. Moreover, we address the problem of choosing an optimal size for a region-ofinterest (ROI) around point landmarks. That is, to reliably localize the landmark position, on the one hand, as much as po...

A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edgebiclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) ...

In this paper we propose a simple but efficient methodology for text detection in video frames. The method is based on the gradient information and edge map selection. In the proposed method we first find the gradient of the image and then enhance the gradient information. We later binarized the enhanced gradient image and select the edges by taking the intersection of the edge map with the bin...