Non-adaptive group testing involves grouping arbitrary subsets of n items into different pools. Each pool is then tested and defective items are identified. A fundamental question...
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth D(G) of a graph G is equal to ...
A map is a connected topological graph cellularly embedded in a surface. For a given graph , its genus distribution of rooted maps and embeddings on orientable and non-orientable s...
Assume that each vertex of a graph G is assigned a nonnegative integer weight and that l and u are nonnegative integers. One wishes to partition G into connected components by del...
A graph G on n vertices is Hamiltonian if it contains a cycle of length n and pancyclic if it contains cycles of length for all 3 ≤ ≤ n. Write α(G) for the independence numbe...