An oriented k-coloring of an oriented graph G (that is a digraph with no cycle of length 2) is a partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the same subset and (ii) all the arcs between any two subsets have the same direction. We survey the main results that have been obtained on oriented graph colorings.

In object detection, non-maximum suppression (NMS) methods are extensively adopted to remove horizontal duplicates of detected dense boxes for generating final instances. However, due the degraded quality detection and not explicit exploration context information, existing NMS via simple intersection-over-union (IoU) metrics tend underperform on multi-oriented long-size objects detection. Disti...

We use results concerning the Smith forms of circulant matrices to identify when cyclically presented groups have free abelianisation and so can be Labelled Oriented Graph (LOG) groups. generalize a theorem Odoni Cremona show that for fixed defining word, whose corresponding representer polynomial has an irreducible factor is not cyclotomic equal ±t, there are at most finitely many n which n-ge...