A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at one of it vertex v consists to complement the edges between the neighborhood and the non-neighborhood of v. Two graphs are Seidel complement equivalent if one can be obtained from the other by a successive application of Seidel complementation. In this paper w...

In this paper, we consider the problems of co-biconnectivity and strong co-connectivity, i.e., computing the biconnected components and the strongly connected components of the complement of a given graph. We describe simple sequential algorithms for these problems, which work on the input graph and not on its complement, and which for a graph on n vertices and m edges both run in optimal O(n +...

We investigate the class of intersection graphs of paths on a grid (VPG graphs), and specifically the relationship between the bending number of a cocomparability graph and the poset dimension of its complement. We show that the bending number of a cocomparability graph G is at most the poset dimension of the complement of G minus one. Then, via Ramsey type arguments, we show our upper bound is...

Many graph search algorithms use a labeling of the vertices to compute an ordering of the vertices. We generalize this idea by devising a general vertex labeling algorithmic process called General Label Search (GLS), which uses a labeling structure which, when specified, defines specific algorithms. We characterize the vertex orderings computable by the basic types of searches in terms of prope...

Let F be an infinite field with characteristic different from two. For a graph G = (V,E) with V = {1, . . . , n}, let S(G;F) be the set of all symmetric n × n matrices A = [ai,j ] over F with ai,j 6= 0, i 6= j if and only if ij ∈ E. We show that if G is the complement of a partial k-tree and m ≥ k + 2, then for all nonsingular symmetric m ×m matrices K over F, there exists an m× n matrix U such...

Weakly-supervised temporal action localization (WTAL) in untrimmed videos has emerged as a practical but challenging task since only video-level labels are available. Existing approaches typically leverage off-the-shelf segment-level features, which suffer from spatial incompleteness and incoherence, thus limiting their performance. In this paper, we tackle problem new perspective by enhancing ...

The present study investigates the pendant number of certain graph classes; complement, line graphs, and total graphs. is minimum end vertices paths in a path decomposition graph. A it into subgraphs; i.e., sequence subset such that endpoints each edge appear one subsets vertex appears an adjacent sub-sequence subsets.