A clique-difference encoding scheme for labelled k-path graphs

AbstractWe present in this paper a codeword for labelled k-path graphs. Structural properties of this codeword are investigated, leading to the solution of two important problems: determining the exact number of labelled k-path graphs with n vertices and locating a hamiltonian path in a given k-path graph in time O(n). The corresponding encoding scheme is also presented, providing linear-time algorithms for encoding and decoding

On some path problems on oriented hypergraphs

The BF-graphs form a particular class of directed hypergraphs. For this important family, several applications are known in data bases and in the artificial intelligence domain. These hypergraphs may also be used to describe the behaviour of concurrent systems. We present here a theoretical analysis of several hyperpath problems for BF-graphs, with emphasis on the acyclic BF-graphs. After briefly explaining the basic concepts of directed hypergraphs, we present an algorithm for finding a BF-path. We next discuss the problem of finding a hyperpath cover, and present a polynomial solution for two constrained hyperpath problems