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Conflict-free coloring of graphs
[article]
2013
arXiv
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We study the conflict-free chromatic number chi_CF of graphs from extremal and probabilistic point of view. ...
In relation to this we study the evolution of the conflict-free chromatic number of the Erdős-Rényi random graph G(n,p) and give the asymptotics for p=omega(1/n). ...
We would like to thank Yury Person for pointing out an error in an earlier version of the proof of Theorem 4. ...
arXiv:1111.5501v2
fatcat:uq3dsoqp25fszma7blbhay35ie
Conflict-Free Coloring of Graphs
2018
SIAM Journal on Discrete Mathematics
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conflict-free coloring of G. ...
Conflict-free coloring has received an increasing amount of attention. Because of the relationship to classic coloring, it is natural to investigate the conflict-free coloring of planar graphs. ...
doi:10.1137/17m1146579
fatcat:uj3b7rzgsbgb3io4j7njd2i6dy
Conflict-Free Coloring of String Graphs
[article]
2019
arXiv
pre-print
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Conflict-free coloring (in short, CF-coloring) of a graph G = (V,E) is a coloring of V such that the neighborhood of each vertex contains a vertex whose color differs from the color of any other vertex ...
., intersection graphs of frames) we prove a tight bound of Θ( n) with respect to the notion of k-CF-coloring (in which the punctured neighborhood of each vertex contains a color that appears at most k ...
Introduction
Background Conflict-free coloring and k-conflict-free coloring of hypergraphs. Definition 1.1. Let H = (V, E) be a hypergraph and let c be a coloring c : V → N. ...
arXiv:1712.04524v2
fatcat:mdd7xxo2azew3cs74sku4rripy
Conflict-Free Coloring of Intersection Graphs
[article]
2017
arXiv
pre-print
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A conflict-free k-coloring of a graph G=(V,E) assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and ...
Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs. ...
Unit square graphs of height 2 are conflict-free 2-colorable. Unit square graphs are conflict-free 4-colorable. ...
arXiv:1709.03876v1
fatcat:ssd4liw3sncb5peerltvokuora
Conflict-Free Coloring: Graphs of Bounded Clique Width and Intersection Graphs
[article]
2022
arXiv
pre-print
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Given an undirected graph G, a conflict-free coloring CFON* (resp. ...
The conflict-free coloring problem asks to find the minimum number of colors required for such a CFON* (resp. ...
We would also like to thank Alexander Hermans for his help on finding a lower bound example for interval graphs. ...
arXiv:2105.08693v3
fatcat:e5d7n67opfgvlorwvownsaa5xe
Proper conflict-free coloring of sparse graphs
[article]
2022
arXiv
pre-print
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2022 pre-print arXiv:2203.16390v1 fatcat:w2wkshuavrbqlbq6ih2htodboe
A proper conflict-free c-coloring of a graph is a proper c-coloring such that each non-isolated vertex has a color appearing exactly once on its neighborhood. ...
., who proved that planar graphs have a proper conflict-free 8-coloring and constructed a planar graph with no proper conflict-free 5-coloring. ...
It is not hard to see that a graph G with mad(G) ≤ c − 1 has a proper conflict-free c-coloring for c ∈ {1, 2}. ...
arXiv:2203.16390v2
fatcat:cxyfunoklvgnbfa3uj6x7x52ae
Conflict-free coloring on closed neighborhoods of bounded degree graphs
[article]
2020
arXiv
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The closed neighborhood conflict-free chromatic number of a graph G, denoted by χ_CN(G), is the minimum number of colors required to color the vertices of G such that for every vertex, there is a color ...
Comput. 2014], Glebov, Szabó and Tardos showed existence of graphs G with χ_CN(G) = Ω(log^2Δ). In this paper, we bridge the gap between the two bounds by showing that χ_CN(G) = O(log^2 Δ). ...
Conflict-free coloring has also been studied in the context of hypergraphs created out of simple graphs. ...
arXiv:2003.05637v3
fatcat:2fvvv3pcwbgdbgmqwbxijviqbe
Parameterized Complexity of Conflict-free Graph Coloring
[article]
2019
arXiv
pre-print
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Given a graph G, a q-open neighborhood conflict-free coloring or q-ONCF-coloring is a vertex coloring c:V(G) →{1,2,... ...
When we replace N(v) by the closed neighborhood N[v], then we call such a coloring a q-closed neighborhood conflict-free coloring or simply q-CNCF-coloring. ...
The research was partially done when the first and second author were associated with Eindhoven University of Technology. ...
arXiv:1905.00305v1
fatcat:wpmqja7okjcmtkoszvdfvzcam4
Three Colors Suffice: Conflict-Free Coloring of Planar Graphs
2017
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
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a planar bipartite graph has a conflict-free k-coloring. ...
A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors ...
Work on this paper was partially supported by the DFG Research Unit "Controlling Concurrent Change", funding number FOR 1800, project FE407/17-2, "Conflict Resolution and Optimization". ...
doi:10.1137/1.9781611974782.127
dblp:conf/soda/AbelADFGHKS17
fatcat:swnroxpghrgcbjwzixamj3gb5i
Parameterized Algorithms for Conflict-free Colorings of Graphs
[article]
2017
arXiv
pre-print
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The conflict-free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict-free. ...
In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. ...
The minimum number of colors needed to conflict-free color the vertices of a hypergraph H is called the conflict-free chromatic number of H. ...
arXiv:1710.00223v1
fatcat:3pecnfkahzbdhdqbrco2vplpwe
Conflict-free coloring on open neighborhoods of claw-free graphs
[article]
2021
arXiv
pre-print
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The 'Conflict-Free Open (Closed) Neighborhood coloring', abbreviated CFON (CFCN) coloring, of a graph G using r colors is a coloring of the vertices of G such that every vertex sees some color exactly ...
As an open question, they asked if the result could be extended to claw-free (K_1,3-free) graphs, which are a superclass of line graphs. ...
Conflict-free chromatic number versus
conflict-free chromatic index. Journal of Graph Theory, 2021.
[EL75] P. Erdős and L. Lovász. ...
arXiv:2112.12173v1
fatcat:ddqsqaqucrftloo2lquegzbiqa
Conflict-Free Coloring of Star-Free Graphs on Open Neighborhoods
[article]
2020
arXiv
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Given a graph, the conflict-free coloring problem on open neighborhoods (CFON) asks to color the vertices of the graph so that all the vertices have a uniquely colored vertex in its open neighborhood. ...
The smallest number of colors required for such a coloring is called the conflict-free chromatic number and denoted χ_ON(G). ...
to Definition 1) of line graphs is O(log ∆). ...
arXiv:2009.06720v1
fatcat:2zzmslartfbkfpnthilhdf5ccq
Conflict-Free Coloring of Intersection Graphs of Geometric Objects
[article]
2017
arXiv
pre-print
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Finally, we present bounds on the number of colors needed for conflict-free colorings of other classes of intersection graphs, including intersection graphs of axis-parallel rectangles and of \rho-fat ...
A conflict-free coloring of a graph is a coloring of its vertices such that the neighborhood (pointed or closed) of each vertex contains a vertex whose color differs from the colors of all other vertices ...
Dozens of papers studied conflict-free colorings of graphs and hypergraphs, mostly arising from geometric objects. See the survey [Smo13] and the references therein for more on CF-colorings. ...
arXiv:1704.02018v1
fatcat:i7l6nnvd6febjje67gbpt6pwjy
Graph unique-maximum and conflict-free colorings
2011
Journal of Discrete Algorithms
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In a conflict-free coloring, in every path of the graph there is a color that appears only once. ...
We investigate the relationship between two kinds of vertex colorings of graphs: uniquemaximum colorings and conflict-free colorings. ...
Conflict-free coloring of graphs with respect to paths is a special case of conflict-free colorings of hypergraphs, first studied in [7, 17] . ...
doi:10.1016/j.jda.2011.03.005
fatcat:cxnfwcqytfgejfbw3cao75jxye
FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain Guarding
[article]
2019
arXiv
pre-print
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We also initiate the study of Strong Conflict-free Coloring of graphs. ...
Given a graph G=(V,E), conflict-free coloring of G refers to coloring a subset of V such that for every vertex v, there is a color that is assigned to exactly one vertex in the closed neighborhood of v ...
We color v with color 1 . The convex layer is now divided into two halves. ...
arXiv:1905.01822v1
fatcat:7kqc2ybmzfgsliti72rtntko2y
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