Dedicated by the other authors to Professor John Maybee on the occasion of his 65th birthday. Abstract. One of the intriguing open problems on competition graphs is determining what digraphs have interval competition graphs. This problem originated in the work of Cohen 5, 6] on food webs. In this paper we consider this problem for the class of loopless symmetric digraphs. The competition graph ...

In path factorization, H. Wang [1] gives the necessary and sufficient conditions for the existence of P_k-factorization of a complete bipartite graph for k, an even integer. Further, Beiling Du [2] extended the work of H. Wang, and studied the P_2k-factorization of complete bipartite multigraph. For odd value of k the work on factorization was done by a number of researchers. P_3-factorization ...

Given a digraph G = (V G,AG), an even factor M ⊆ AG is a subset of arcs that decomposes into a collection of node-disjoint paths and even cycles. Even factors in digraphs were introduced by Geleen and Cunningham and generalize path matchings in undirected graphs. Finding an even factor of maximum cardinality in a general digraph is known to be NP-hard but for the class of odd-cycle symmetric di...

We study the problem of routing symmetric demand pairs in planar digraphs. The input consists of a directed planar graph G = (V, E) and a collection of k source-destination pairs M = {s1t1, . . . , sktk}. The goal is to maximize the number of pairs that are routed along disjoint paths. A pair siti is routed in the symmetric setting if there is a directed path connecting si to ti and a directed ...

When joined to a stipulated neighborhood digraph, an objective function deÞned on the solution space of a real combinatorial optimization problem forms a landscape. Grover shows that landscapes satisfying a certain difference equation have properties favorable to local search. Studying only symmetric and regular neighborhood digraphs, Stadler deÞnes elementary landscapes as those which can be r...

A strongly connected digraph D of order n is primitive (aperiodic) provided the greatest common divisor of its directed cycle lengths equals 1. For such a digraph there is a minimum integer t, called the exponent of D, such that given any ordered pair of vertices x and y there is a directed walk from x to y of length t. The exponent of D is the largest of n ‘generalized exponents’ that may be a...

In this paper we prove that if a finite reflexive digraph admits Gumm operations, then it also admits a near unanimity operation. This is a generalization of similar results obtained earlier for posets and symmetric reflexive digraphs by the second author and his collaborators. In the special case of reflexive digraphs our new result confirms a conjecture of Valeriote that states that any finit...

In this paper, we present a linear time algorithm for constructing linkless drawings of series parallel digraphs with maximum number of symmetries. Linkless drawing in three dimensions is a natural extension to planar drawing in two dimensions. Symmetry is one of the most important aesthetic criteria in graph drawing. More specifically, we present two algorithms: a symmetry finding algorithm wh...