the colorful paths and rainbow paths have been considered by severalauthors.a colorful directed path in a digraph $g$ is a directed path with $chi(g)$ vertices whose colors are different. a $v$-colorful directed path is such a directed path, starting from $v$. we prove that for a given $3$-regular triangle-free digraph $g$ determining whether there is a proper $chi(g)$-coloring of $g$such that ...

Abstract In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a graph $$G=(V,E)$$ G = ( V , E ) and set $$T \subseteq V$$ T ...

We describe various path homology theories constructed for a directed hypergraph. introduce the category of hypergraphs and notion homotopy in this category. Also, we investigate functoriality invariance introduced groups. provide examples computation these

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

We present a linear time algorithm to greedily orient the edges of a path graph model to obtain a directed path graph model (when possible). Moreover we extend this algorithm to find an odd sun when the method fails. This algorithm has several interesting consequences concerning the relationship between path graphs and directed path graphs. One is that for a directed path graph, path graph mode...

Learning from multi-relational domains has gained increasing attention over the past few years. Inductive logic programming (ILP) systems, which often rely on hill-climbing heuristics in learning first-order concepts, have been a dominating force in the area of multi-relational concept learning. However, hill-climbing heuristics are susceptible to local maxima and plateaus. In this paper, we sh...