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We also present two algorithms for restricted classes of graphs: first, an algorithm with time complexity linear in the number of edges that finds such a partition for all graphs which contain no isolated vertices and no vertex adjacent to more than two vertices of degree one; and second, an algorithm which determines if such a partition exists for a tree with n vertices in time O(n2).
Graph C ∗ -algebras of countable graphs which contain infinite emitters were introduced in [63] (2000); these motivated the definition of Leavitt path algebras of such graphs in [9] (2006).
In particular we shall consider the classes of extended P4-laden [16], p-trees [3] (graphs which contain exactly n−3 P4's) and (q,q−3 -graphs,q−3 -graphsuch that no set of at most q≥7ertices induces more that q−3 distincts P4's.
In particular we shall consider the classes of extended P4-laden graphs, p-trees (graphs which contain exactly n−3 P4's) and (q,q−3 -graphs,q−3 -graphsthat no set of at most q≥7erticesuchduces more that q−3 distinotset4's.
Because BNs aim to represent the joint probability distribution (in our case for the expression levels of p genes) the corresponding graphical representation is limited to graphs which contain no cycles.
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In this paper we give a complete linear description of the dominant of the associated polytope in a class of graphs called perfectly Steiner 2-edge connected graphs, which contains series parallel graphs.
The Web is just one example of a hierarchical tree structure with links ''back up the tree" i.e. a directed graph which contains cycles.
Pseudo-minimal and minimal sensor sets are organized into an oriented graph which contains all the possible reconfiguration paths for which the system remains observable.
Assume that, given a key sharing graph which contains a spanning tree, any designated player wishes to broadcast a message to all the other players securely against an eavesdropper.
The first step is determining a suitable space graph which contains all critical points of a real algebraic space curve C implicitly defined as the complete intersection of two surfaces.
A triangle-free graph is a graph which contains no triangle.
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