
Complexity of treecoloring interval graphs equitably
An equitable treekcoloring of a graph is a vertex kcoloring such that...
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Equitable treeO(d)coloring of ddegenerate graphs
An equitable treekcoloring of a graph is a vertex coloring on k colors...
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Lineartime algorithm for vertex 2coloring without monochromatic triangles on planar graphs
In the problem of 2coloring without monochromatic triangles (or triangl...
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Equitable vertex arboricity of ddegenerate graphs
A minimization problem in graph theory socalled the equitable treecolo...
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NonMonochromatic and ConflictFree Coloring on Tree Spaces and Planar Network Spaces
It is well known that any set of n intervals in R^1 admits a nonmonochr...
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Maximizing coverage while ensuring fairness: a tale of conflicting objective
Ensuring fairness in computational problems has emerged as a key topic d...
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Distributed Graph Coloring: An Approach Based on the Calling Behavior of Japanese Tree Frogs
Graph coloring, also known as vertex coloring, considers the problem of ...
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On λbackbone coloring of cliques with tree backbones in linear time
A λbackbone coloring of a graph G with its subgraph (also called a backbone) H is a function c V(G) →{1,…, k} ensuring that c is a proper coloring of G and for each {u,v}∈ E(H) it holds that c(u)  c(v) ≥λ. In this paper we propose a way to color cliques with tree and forest backbones in linear time that the largest color does not exceed max{n, 2 λ} + Δ(H)^2 ⌈logn⌉. This result improves on the previously existing approximation algorithms as it is (Δ(H)^2 ⌈logn⌉)absolutely approximate, i.e. with an additive error over the optimum. We also present an infinite family of trees T with Δ(T) = 3 for which the coloring of cliques with backbones T require to use at least max{n, 2 λ} + Ω(logn) colors for λ close to n/2.
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