A graph G is said to be F-saturated if G does not contain a copy of F as a subgraph and G+ e contains a copy of F as a subgraph for any edge e contained in the complement of G. Erdős et al. in [A problem in graph theory, Amer. Math. Monthly 71 (1964) 1107–1110.] determined the minimum number of edges, sat(n, F ), such that a graph G on n vertices must have when F is a t-clique. Later, Ollmann [...

The classical stability theorem of Erdős and Simonovits states that, for any fixed graph with χ(H) = k+ 1 ≥ 3, the following holds: every n-vertex graph that is H-free and has within o(n2) of the maximal possible number of edges can be made into the k-partite Turán graph by adding and deleting o(n2) edges. In this paper, we prove sharper quantitative results for graphs H with a critical edge, b...

A multipartite or c-partite tournament is an orientation of a complete c-partite graph. Lu and Guo (submitted for publication) [3] recently introduced strong quasi-Hamiltonianconnectivity of a multipartite tournament D as follows: For any two distinct vertices x and y ofD, there is a pathwith at least one vertex from each partite set ofD from x to y and from y to x. We obtain the definition for...

Let τ(H) be the cover number and ν(H) be the matching number of a hypergraph H. Ryser conjectured that every r-partite hypergraph H satisfies the inequality τ(H) ≤ (r − 1)ν(H). This conjecture is open for all r ≥ 4. For intersecting hypergraphs, namely those with ν(H) = 1, Ryser’s conjecture reduces to τ(H) ≤ r − 1. Even this conjecture is extremely difficult and is open for all r ≥ 6. For infi...

Slovenija Abstract A partial extension of the results in 1], where 2-arc-transitive cir-culants are classiied, is given. It is proved that a 2-arc-transitive Cayley graph of a dihedral group is either a complete graph or a bi-partite graph.

We present a novel approach for robust localization of multiple people observed using a set of static cameras. We use this location information to generate a visualization of the virtual offside line in soccer games. To compute the position of the offside line, we need to localize players′ positions, and identify their team roles. We solve the problem of fusing corresponding players′ positional...

An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D. An edge domatic partition of a graph C=(V, E) is a collection of pairwise-disjoint edge dominating sets of G whose union is E. The maximum size of an edge domatic partition of G is called the edge domatic number. In this paper, we study the edge domatic number of the complete parti...

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s, k)-polar if there exists a partition A, B of its vertex set such that A induces a complete s-partite graph (i.e., a collection of at most s disjoint stable sets with complete links between all sets) and B a disjoint union of at most k cliques (i....

Let G be a bipartite graph, and let λe, λi be two parallel convex curves; we study the question about whether G admits a planar straight line drawing such that the vertices of one partite set of G lie on λe and the vertices of the other partite set lie on λi. A characterization is presented that gives rise to linear time testing and drawing algorithms.