In the graph searching problem, we are given a graph whose edges are all "contaminated", and, via a sequence of "steps" using "searchers", we want to obtain a state of the graph in which all edges are simultaneously "clear". ...

We prove that if P superA[k] = P superA[k+1] for some k and an arbitrary set A, then A is reducible to its complement under a relativized nondeterministic conjunctive reduction. This result shows the first known property ...

We study the complexity of sets that are at the same time self-reducible and sparse or m-reducible to sparse sets. We show that sets of this kind are low for the complexity clases [delta sub 2 super p], [fi sub 2 super p], ...

An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . . , |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels ...

A k -coloring of a graph G is a k -partition ¿ = { S 1 ,...,S k } of V ( G ) into independent sets, called colors . A k -coloring is called neighbor-locating if for every pair of vertices u,v belonging to the same color S ...

A partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other ...