Let D be a directed graph of order n. An anti-directed (hamiltonian) cycleH inD is a (hamiltonian) cycle in the graph underlyingD such that no pair of consecutive arcs in H form a directed path in D. In this paper we give sufficient conditions for the existence of anti-directed hamiltonian cycles. Specifically, we prove that a directed graph D of even order n with minimum indegree and outdegree...

In graduate school, my research has focused on problems in extremal directed graph theory. A 100-year old theorem of Mantel answers the question: what is the smallest value k so that, if every vertex in an undirected simple graph on n vertices has more than k edges coming out of it, the graph must contain a triangle? Mantel, and subsequently Turán, proved that this value is n/2. Their result is...

We study a class of matrix function algebras, here denoted T (Cn). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T (Cn). We use point derivations and information about n×n matrices to show that every T (Cn)-valued derivation on T (Cn) is inner. Certain matrix function algebras arise in some standard constructions...

The growing interest in graph deep learning has led to a surge of research focusing on various characteristics graph-structured data. Directed graphs have generally been treated as incidental definitions the more general class undirected graphs. implicit imbalance some problems also proves difficult tackle. Moreover, body work begun grow that considers how learn signals structured edges In this...

A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on n vertices contains a feedback vertex set (FVS) of size at most k, in time 2k!O(n). This is the first fixed parameter tractable algorithm for FVS that applies to both directed and undirected graphs.