Suppose that D is an acyclic orientation of a graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let dmin(G) (dmax(G)) denote the minimum (maximum) of the number of dependent arcs over all acyclic orientations of G. We call G fully orientable if G has an acyclic orientation with exactly d dependent arcs for every d satisfying dmin(G) 6 d 6 dmax(G). A graph G is c...

Suppose that D is an acyclic orientation of the graph G. An arc of D is dependent if its reversal creates a directed cycle. Let d(D) denote the number of dependent arcs in D. Define dmin(G) (dmax(G)) to be the minimum (maximum) number of d(D) over all acyclic orientations D of G. We call G fully orientable if G has an acyclic orientation with exactly k dependent arcs for every k satisfying dmin...

To every directed graph G one can associate a complex (G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to studying some interesting representations of the symmetric group and corresponds (via Stanley-Reisner correspondence) to an interesting quotient ring. Our main ...

This paper investigates obviously strategyproof (OSP) implementation of the popular top trading cycles (TTC) and deferred acceptance (DA) mechanisms. Introduced by Li (2016), obvious strategyproofness requires not only that truthful reporting be a dominant strategy, but also that this be obvious to agents who may have limited abilities of contingent reasoning. We characterize the full class of ...

Let Pn be the path graph on n vertices. In this paper, we consider the distance graphs G(Pn, D), where the distance set D ⊆ {1, 2, 3, . . . , n− 1}. We characterize the distance set D for which G(Pn, D) is one of path, cycle, wheel, regular, bipartite, acyclic, Cr-free, K1,r-free, or having isolated vertices.

We present a method for constructing dynamical systems with robust, stable limit cycles in arbitrary dimensions. Our approach is based on a correspondence between dynamics in a class of differential equations and directed graphs on the n-dimensional hypercube (n-cube). When the directed graph contains a certain type of cycle, called a cyclic attractor, then a stable limit cycle solution of the ...

We show that digraphs with no transitive tournament on $3$ vertices and in which every induced directed cycle has length can have arbitrarily large dichromatic number. This answers the negative a question of Carbonero, Hompe, Moore, Spirkl (and strengthens one their results).

In this paper we investigate the basic problem of Exploration of a graph by a group of identical mobile computational entities, called robots, operating autonomously and asynchronously. In particular we are concerned with what graphs can be explored, and how, if the robots do not remember the past and have no explicit means of communication. This model of robots is used when the spatial univers...

The activities of the nuclear RNA polymerases I and II have been investigated in cells of Sacharomyces cerevisiae at G(1), S, early G(2), and late G(2) stages of the cell cycle. The results show that the ratio of the activities of the two enzymes is different at these four stages, indicating that the two RNA polymerases are regulated independently during the cell cycle. The specific activity of...

Proliferation of mammalian cardiomyocytes ceases around birth when a transition from hyperplastic to hypertrophic myocardial growth occurs. Previous studies demonstrated that directed expression of the transcription factor E2F1 induces S-phase entry in cardiomyocytes along with stimulation of programmed cell death. Here, we show that directed expression of E2F2 and E2F4 by adenovirus mediated g...