Networks communicating for each pairing of terminals

Abstract

Let G be a multigraph of maximum degree A and with a set o f t vertices of degree one, called terminals. We call G a (A, t)-network if for any pairing of its terminals there exist edge-disjoint paths in G between those pairs ( t is even). The concept of (A, [)-networks is introduced to model the situation when switching processors having A ports are to be connected in such a way that simultaneous communication is possible for any pairing of the free ports. We establish some properties of (A, t)-nerwwks. In particular, we investigate optimal (or near-optimal) networks and obtain lower and upper bounds on the function n(A, t ) , the minimum number of interior nodes a (A, t)-network can have.

Terminal-pairability in complete bipartite graphs with non-bipartite demands

“…The terminal-pairability problem arose as a theoretical framework for the practical problem of constructing high throughput packet switching networks. The problem was originally studied by Csaba, Faudree, Gyárfás, Lehel, and Schelp [7]. Their research served as a substrate for further theoretical studies by Gyárfás and Schelp [18] and Kubicka, Kubicki, and Lehel [26].…”

An improved upper bound on the maximum degree of terminal-pairable complete graphs

“…The same authors proved in [2] that K q n can be realized in K n if q ≤ n 4+2 √ 3 , and conjectured that if n ≡ 2 (mod 4), then the upper bound of n/2 is attainable, that is, K n is terminal-pairable with respect to K n/2 n . This conjecture is also stated in [4].…”

Length‐constrained path‐matchings in graphs

“…The relationship between the path-matching problem (with a slightly different definition) and the matroid intersection problem was studied by Cunningham and Geelen [4]. Also, several related problems were studied by Csaba et al [3] and Yinnone [14]. A generalization of this problem called S-paths was introduced by Mader [10] (see also Schrijver [11]).…”