Let k be a nonnegative integer, and let mk = 4(k+1)(k+3) k2+6k+6 . We prove that every simple graph with maximum average degree less than mk decomposes into a forest and a subgraph with maximum degree at most k. It follows that every simple graph with maximum average degree less than mk has game coloring number at most 4 + k.

The local boxicity of a graph G, denoted by lbox(G), is the minimum positive integer l such that G can be obtained using intersection k (where k≥l) interval graphs where each vertex appears as non-universal in at most these graphs. Let on n vertices having m edges. Δ denote maximum degree G. We show that, lbox(G)≤213log⁎⁡ΔΔ. lbox(G)∈O(nlog⁡n). lbox(G)≤(213log⁎⁡m+2)m. its product dimension. This...

extended abstract 1. introduction temperature leaves undeniable effects on human activities and natural processes. the analysis of average maximum temperature and the highest temperatures related to the heat wave phenomenon is of great importance. the most important goals of this study include the investigation of the geographical distribution of the maximum average temperatures and extreme tem...

An r-dynamic k-coloring of a graph G is a proper k-coloring φ such that for any vertex v, v has at least min{r, degG(v)} distinct colors in NG(v). The r-dynamic chromatic number χr(G) of a graph G is the least k such that there exists an r-dynamic k-coloring of G. The list r-dynamic chromatic number of a graph G is denoted by chr(G). Recently, Loeb, Mahoney, Reiniger, and Wise showed that the l...