We consider the one-variable characteristic polynomial p(G; ) in two settings. When G is a rooted digraph, we show that this polynomial essentially counts the number of sinks in G. When G is a rooted graph, we give combinatorial interpretations of several coe/cients and the degree of p(G; ). In particular, |p(G; 0)| is the number of acyclic orientations of G, while the degree of p(G; ) gives th...

Prefetching constitutes a valuable tool toward the goal of efficient Web surfing. As result, estimating amount resources that need to be preloaded during surfer's browsing becomes an important task. In this regard, prefetching can modeled as two-player combinatorial game (Fomin et al. (2014) [6] ), where surfer and marker alternately play on given graph (representing graph). During its turn, ch...