Constructing some regular graph with a given girth, a given degree and the fewest possible vertices is a hard problem. This problem is called the cage graph problem and has some l...
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is ide...
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at m...
We show that in any graph G on n vertices with d(x) + d(y) n for any two nonadjacent vertices x and y, we can fix the order of k vertices on a given cycle and find a hamiltonian c...
Let C be a code of length n over an alphabet of q letters. A codeword y is called a descendant of a set of t codewords {x1 , . . . , xt } if yi {x1 i , . . . , xt i} for all i = ...