a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology [9], and the framework through which it was studied, we introduce the linear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be linearly colored in polynomial time by proposing a simple linear coloring ...

Register allocation has long been formulated as a graph coloring problem, coloring the conflict graph with physical registers. Such a formulation does not fully capture the goal of the allocation, which is to minimize the traffic between registers and memory. Linear scan has been proposed as an alternative to graph coloring, but in essence, it can be viewed as a greedy algorithm for graph color...

We prove that the intersection hypergraph of a family of n pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with 4 colors and a conflict-free coloring with O(log n) colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of n regions with linear union complexity with respect to a ...