TL;DR
This paper investigates properties of minimal senders in graph theory, proving their connectedness and demonstrating the unbounded diameters of minimal graphs with specific connectivity and cycle properties.
Contribution
It establishes that all minimal senders are connected and shows there is no upper limit on the size of minimal graphs with certain connectivity and cycle conditions.
Findings
Connectedness of minimal senders proved
Existence of arbitrarily large minimal graphs with specified properties
No upper bound on diameters of (G,H)-minimal graphs
Abstract
In this paper we prove that if a pair of graphs G,H have senders, then they necessarily have connected minimal senders; we also prove that given two fixed graphs that are either 3-connected or triangles there are minimal (G,H)-senders with arbitrarily distant signal edges and (G,H)-minimal graphs with arbitrarily large cycles, thus showing there is no upper bound for the diameters of (G,H)-minimal graphs.
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Taxonomy
TopicsCooperative Communication and Network Coding · graph theory and CDMA systems · Coding theory and cryptography