Abstract-We present ETCH, efficient channel hopping based MAC-layer protocols for communication rendezvous in Dynamic Spectrum Access (DSA) networks. Compared to the existing solutions, ETCH fully utilizes spectrum diversity in communication rendezvous by allowing all the rendezvous channels to be utilized at the same time. We propose two protocols, SYNC-ETCH, which is a synchronous protocol assuming DSA nodes can synchronize their channel hopping processes, and ASYNC-ETCH, which is an asynchronous protocol not relying on global clock synchronization. Our theoretical analysis and ns-2 based evaluation show that ETCH achieves better performances of timeto-rendezvous and throughput than the existing work.

A graph is k-linked if for every list of 2k vertices {s 1 , . . . , s k , t 1 , . . . , t k }, there exist internally disjoint paths P 1 , . . . , P k such that each P i is an s i , t i -path. We consider degree conditions and connectivity conditions sufficient to force a graph to be k-linked.Let D(n, k) be the minimum positive integer d such that every n-vertex graph with minimum degree at least d is k-linked and let R(n, k) be the minimum positive integer r such that every n-vertex graph in which the sum of degrees of each pair of non-adjacent vertices is at least r is k-linked. The main result of the paper is finding the exact values of D(n, k) and R(n, k) for every n and k. Thomas and Wollan [14] used the bound D(n, k) (n + 3k)/2 − 2 to give sufficient conditions for a graph to be k-linked in terms of connectivity. Our bound allows us to modify the Thomas-Wollan proof slightly to show that every 2k-connected graph with average degree at least 12k is k-linked.

a b s t r a c tAn open-locating-dominating set (OLD-set) is a subset of vertices of a graph such that every vertex in the graph has at least one neighbor in the set and no two vertices in the graph have the same set of neighbors in the set. This is an analogue to the well-studied identifying code in the literature. In this paper, we prove that the optimal density of an OLD-set for the infinite triangular grid is 4/13.

Abstract. The strong chromatic index of a multigraph is the minimum k such that the edge set can be k-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gyárfás, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.This paper is to appear in European J. Combin. 51 (2016) 380-397.Mathematics Subject Classification: 05C15 (05C10)