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Displaying 1101 –
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To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.
Our short note gives the affirmative answer to one of Fishburn’s questions.
Let and , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal antichains...
A subset of the vertex set of a graph is called dominating in , if for each there exists adjacent to . An antidomatic partition of is a partition of , none of whose classes is a dominating set in . The minimum number of classes of an antidomatic partition of is the number of . Its properties are studied.
It is well known that given a Steiner triple system one can define a quasigroup operation upon its base set by assigning for all and , where is the third point in the block containing the pair . The same can be done for Mendelsohn triple systems, where is considered to be ordered. But this is not necessarily the case for directed triple systems. However there do exist directed triple systems, which induce a quasigroup under this operation and these are called Latin directed triple systems....
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