we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

We discuss a new algorithmic type of problem in random graphs studying the minimum number of queries one has to ask about adjacency between pairs of vertices of a random graph G ∼ G(n, p) in order to find a subgraph which possesses some target property with high probability. In this paper we focus on finding long paths in G ∼ G(n, p) when p = 1+ε n for some fixed constant ε > 0. This random gra...

Given a graph G and an integer k, the H-free Edge Editing problem is to find whether there exist at most k pairs of vertices in such that changing adjacency results without any induced copy H. Nontrivial polynomial kernels are known for some graphs H with 4 vertices, but starting from 5 only if either complete or empty. This suggests conjecture no other least where admits kernel. Towards this g...