In this work, we establish a general relationship between the enumeration of weighted directed paths and skew Schur functions, extending work by Bousquet-M\'elou, who expressed generating functions discrete excursions in terms rectangular functions.

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Given a graph G, the associahedron is simple convex polytope whose face poset based on connected subgraphs of G. With additional assignment color palette, we define colorful associahedron, show it to be collection abstract polytopes, and explore its properties.

A digraph H is infused in a digraph G if the vertices of H are mapped to vertices of G (not necessarily distinct), and the edges of H are mapped to edge-disjoint directed paths of G joining the corresponding pairs of vertices of G. The algorithmic problem of determining whether a fixed graph H can be infused in an input graph G is polynomial-time solvable for all graphs H (using paths instead o...