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Conflict-free coloring of graphs
[article]

2013
*
arXiv
*
pre-print

We study the

arXiv:1111.5501v2
fatcat:uq3dsoqp25fszma7blbhay35ie
*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. ...##
###
Conflict-Free Coloring of Graphs

2018
*
SIAM Journal on Discrete Mathematics
*

*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*. ...

##
###
Conflict-Free Coloring of String Graphs
[article]

2019
*
arXiv
*
pre-print

*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. ...

##
###
Conflict-Free Coloring of Intersection Graphs
[article]

2017
*
arXiv
*
pre-print

A

arXiv:1709.03876v1
fatcat:ssd4liw3sncb5peerltvokuora
*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*. ...##
###
Conflict-Free Coloring: Graphs of Bounded Clique Width and Intersection Graphs
[article]

2022
*
arXiv
*
pre-print

Given an undirected

arXiv:2105.08693v3
fatcat:e5d7n67opfgvlorwvownsaa5xe
*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*. ...##
###
Proper conflict-free coloring of sparse graphs
[article]

2022
*
arXiv
*
pre-print

A proper

arXiv:2203.16390v2
fatcat:cxyfunoklvgnbfa3uj6x7x52ae
*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}. ...##
###
Conflict-free coloring on closed neighborhoods of bounded degree graphs
[article]

2020
*
arXiv
*
pre-print

The closed neighborhood

arXiv:2003.05637v3
fatcat:2fvvv3pcwbgdbgmqwbxijviqbe
*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*. ...##
###
Parameterized Complexity of Conflict-free Graph Coloring
[article]

2019
*
arXiv
*
pre-print

Given a

arXiv:1905.00305v1
fatcat:wpmqja7okjcmtkoszvdfvzcam4
*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. ...##
###
Three Colors Suffice: Conflict-Free Coloring of Planar Graphs

2017
*
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
*

a planar bipartite

doi:10.1137/1.9781611974782.127
dblp:conf/soda/AbelADFGHKS17
fatcat:swnroxpghrgcbjwzixamj3gb5i
*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". ...##
###
Parameterized Algorithms for Conflict-free Colorings of Graphs
[article]

2017
*
arXiv
*
pre-print

The

arXiv:1710.00223v1
fatcat:3pecnfkahzbdhdqbrco2vplpwe
*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. ...##
###
Conflict-free coloring on open neighborhoods of claw-free graphs
[article]

2021
*
arXiv
*
pre-print

The '

arXiv:2112.12173v1
fatcat:ddqsqaqucrftloo2lquegzbiqa
*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. ...##
###
Conflict-Free Coloring of Star-Free Graphs on Open Neighborhoods
[article]

2020
*
arXiv
*
pre-print

Given a

arXiv:2009.06720v1
fatcat:2zzmslartfbkfpnthilhdf5ccq
*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 ∆). ...##
###
Conflict-Free Coloring of Intersection Graphs of Geometric Objects
[article]

2017
*
arXiv
*
pre-print

Finally, we present bounds on the number

arXiv:1704.02018v1
fatcat:i7l6nnvd6febjje67gbpt6pwjy
*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*. ...##
###
Graph unique-maximum and conflict-free colorings

2011
*
Journal of Discrete Algorithms
*

In a

doi:10.1016/j.jda.2011.03.005
fatcat:cxnfwcqytfgejfbw3cao75jxye
*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] . ...##
###
FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain Guarding
[article]

2019
*
arXiv
*
pre-print

We also initiate the study

arXiv:1905.01822v1
fatcat:7kqc2ybmzfgsliti72rtntko2y
*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. ...
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