On the size of identifying codes in triangle-free graphs

In an undirected graph $G$, a subset $C\subseteq V(G)$ such that $C$ is a dominating set of $G$, and each vertex in $V(G)$ is dominated by a distinct subset of vertices from $C$, is called an identifying code of $G$. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph $G$, let \M(G) be the minimum cardinality of an identifying code in $G$. In this paper, we show that for any connected identifiable triangle-free graph $G$ on $n$ vertices having maximum degree $\Delta\geq 3$, \M(G)\le n-\tfrac{n}{\Delta+o(\Delta)}. This bound is asymptotically tight up to constants due to various classes of graphs including $(\Delta-1)$-ary trees, which are known to have their minimum identifying code of size $n-\tfrac{n}{\Delta-1+o(1)}$. We also provide improved bounds for restricted subfamilies of triangle-free graphs, and conjecture that there exists some constant $c$ such that the bound \M(G)\le n-\tfrac{n}{\Delta}+c holds for any nontrivial connected identifiable graph $G$

OTF2: Open Trace Format Version 2 (v3.0.2)

The Open Trace Format Version 2 (OTF2) is a highly scalable, memory efficient event trace data format plus support library. It is the standard trace format for Scalasca, Vampir, and Tau and is open for other tools.OTF2 is available under the 3-clause BSD Open Source license.OTF2 is the common successor format for the Open Trace Format (OTF) and the Epilog trace format. It preserves the essential features as well as most record types of both and introduces new features such as support for multiple read/write substrates, in-place time stamp manipulation, and on-the-fly token translation. In particular, it will avoid copying during unification of parallel event streams