A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Conflict-Free Colouring of Subsets
[article]

2022
*
arXiv
*
pre-print

We introduce and study

arXiv:2207.01041v1
fatcat:ysbha4zjefhd7efm2rffqf3opq
*conflict*-*free**colourings**of*t-*subsets*in hypergraphs. ... (iii) We also show that there is no general bound on the t-*subset**conflict*-*free*chromatic number as a function*of*the standard*conflict*-*free*chromatic number already for t=2. ...*Conflict*-*Free**Colouring**of**Subsets*...##
###
Perfect Resolution of Strong Conflict-Free Colouring of Interval Hypergraphs
[article]

2021
*
arXiv
*
pre-print

The k-Strong

arXiv:1707.05071v4
fatcat:qi2cfpqrwvahdjjuvlx264tvxe
*Conflict*-*Free*(k-SCF, in short)*colouring*problem seeks to find a*colouring**of*the vertices*of*a hypergraph H using minimum number*of**colours*so that in every hyperedge e*of*H, there are at ... least min{|e|,k} vertices whose*colour*is different from that*of*all other vertices in e. ... I ℓ } based on t and the vertex*colouring*as follows: the set I i consists*of*all those hyperedges I ∈ I such that the*colour**of*t(I) is i. ...##
###
Conflict-Free Colourings of Graphs and Hypergraphs

2009
*
Combinatorics, probability & computing
*

A

doi:10.1017/s0963548309990290
fatcat:47cm2tiqqvefdp4jdq7phjjx3q
*colouring**of*the vertices*of*a hypergraph H is called*conflict*-*free*if each hyperedge E*of*H contains a vertex*of*'unique'*colour*that does not get repeated in E. ... The smallest number*of**colours*required for such a*colouring*is called the*conflict*-*free*chromatic number*of*H, and is denoted by χ CF (H). ...*Conflict*-*Free**Colourings**of*Graphs and Hypergraphs ...##
###
Conflict-free vertex connection number at most 3 and size of graphs

2019
*
Discussiones Mathematicae Graph Theory
*

A path in a vertex-

doi:10.7151/dmgt.2211
fatcat:5unwwpaxxrdjrcmxvqlr7ipmay
*coloured*graph is called*conflict*-*free*if there is a*colour*used on exactly one*of*its vertices. ... A vertex-*coloured*graph is said to be*conflict*-*free*vertex-connected if any two distinct vertices*of*the graph are connected by a*conflict*-*free*vertex-path. ... The*conflict*-*free*connection number*of*a connected graph G, denoted by cf c(G), is defined as the smallest number*of**colours*in order to make it*conflict*-*free*connected. ...##
###
On conflict-free chromatic guarding of simple polygons
[article]

2020
*
arXiv
*
pre-print

This is also known as the

arXiv:1904.08624v3
fatcat:i5kh5en7src2zhdr7ulic5gcc4
*conflict*-*free*chromatic guarding problem with vertex guards, and is motivated, e.g., by the problem*of*radio frequency assignment to sensors placed at the polygon vertices. ... We study the problem*of**colouring*the vertices*of*a polygon, such that every viewer in it can see a unique*colour*. The goal is to minimise the number*of**colours*used. ... We recall the following property from the proof*of*Proposition 6.1: (i) In any*conflict*-*free*2-*colouring**of*the bowl there is a guard (or two) placed at the door. ...##
###
Invariant measures in simple and in small theories
[article]

2022
*
arXiv
*
pre-print

groups and

arXiv:2105.07281v2
fatcat:iekcizjczvcbva5tbxliws45s4
*of*definable groups, and prove some positive results about small theories, including the definable amenability*of*definable groups, and nontriviality*of*the graded Grothendieck ring. ... We give examples*of*(i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measure mu, and (ii) a definable ...*Colourings*and*free*actions. We fix a*free*action*of*F 5 on a set X. As above, we will denote by {f 1 , f 2 , f 3 , g 1 , g 2 } a system*of**free*generators for the*free*group F 5 . ...##
###
Linear combinations of heuristics for examination timetabling

2011
*
Annals of Operations Research
*

Some recent work has demonstrated the superiority

doi:10.1007/s10479-011-0854-y
fatcat:2jf7dk7s2rcpjkipdiwd7y7gni
*of*combining a number*of*different heuristics for vertex and*colour*selection. ... Most*of*this work used a single heuristic to measure the difficulty*of*a vertex. Relatively less attention has been paid to select an appropriate*colour*for the selected vertex. ... The weight*of*an edge between two vertices represents the number*of*students taking both corresponding exams.*Conflict*-*free**colourings*represent timetables that satisfy the hard constraint. ...##
###
Perfect Resolution of Conflict-Free Colouring of Interval Hypergraphs

2020
*
Symposium on Theoretical Aspects of Computer Science
*

Given a hypergraph H, the

doi:10.4230/lipics.stacs.2020.52
dblp:conf/stacs/DhannyaN20
fatcat:gukkufd6afhv3pwuzccy5ksnyu
*conflict*-*free**colouring*problem is to*colour*vertices*of*H using minimum*colours*so that in every hyperedge e*of*H, there is a vertex whose*colour*is different from that*of*all ... Our results are on a variant*of*the*conflict*-*free**colouring*problem considered by Cheilaris et al. ... [4] and is a variant*of*a well-studied hypergraph*colouring*problem known as the*Conflict*-*Free**colouring*problem. ...##
###
A Lower Bound on the Area of a 3-Coloured Disc Packing

2007
*
Canadian Conference on Computational Geometry
*

Motivated by the problem

dblp:conf/cccg/BrassHLL07
fatcat:dwo4ylxgk5av3mncrpk7czoanm
*of*channel-assignment for wireless access points, we consider a variant where the selected*subset**of*discs must be 3-*colourable*, with discs*of*the same*colour*pairwisedisjoint. ... Given a set*of*unit-discs in the plane with union area A, what fraction*of*A can be covered by selecting a pairwise disjoint*subset**of*the discs? Rado conjectured 1/4 and proved 1/4.41. ... There is also work on online algorithms for*conflict*-*free**colouring*[8] , and on conflictfree*colouring**of*regions other than discs [10] . ...##
###
A Lower Bound on the Area of a 3-Coloured Disk Packing
[article]

2008
*
arXiv
*
pre-print

Motivated by the problem

arXiv:0804.1173v1
fatcat:cw6trtnlovagpmqv6wuxjhebxi
*of*channel-assignment for wireless access points, in which use*of*3 channels is a standard practice, we consider a variant where the selected*subset**of*disks must be 3-*colourable*... with disks*of*the same*colour*pairwise-disjoint. ... Keshav, University*of*Waterloo, and the work was initiated at the 5th ...##
###
An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings
[article]

2012
*
arXiv
*
pre-print

An optimal algorithm is presented about

arXiv:1203.2414v1
fatcat:wsfhx4rcvrhqlhcdt2ogtu7id4
*Conflict*-*Free*Coloring for connected subgraphs*of*tree*of*rings. Suppose the number*of*the rings in the tree is |T| and the maximum length*of*rings is |R|. ... A presented algorithm in [1] for a Tree*of*rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors. ... ACKNOWLEDGEMENTS This research has been supported by the business training center*of*tabriz,Iran. ...##
###
Colouring graphs with no induced six-vertex path or diamond
[article]

2021
*
arXiv
*
pre-print

In this paper we show that the chromatic number

arXiv:2106.08602v1
fatcat:pl3t44exu5elxorxxjb43hhl3m
*of*a (P_6, diamond)-*free*graph G is no larger than the maximum*of*6 and the clique number*of*G. ... We do this by reducing the problem to imperfect (P_6, diamond)-*free*graphs via the Strong Perfect Graph Theorem, dividing the imperfect graphs into several cases, and giving a proper*colouring*for each ... By (12) , B and C do not*conflict*. By (11) (13) , this is a proper*colouring**of*F . By (18) , F and C do not*conflict*. By (17) , B 2,3 and F \ F 5 do not*conflict*. ...##
###
Are scale-free regulatory networks larger than random ones?
[article]

2005
*
arXiv
*
pre-print

Network

arXiv:q-bio/0501027v1
fatcat:cgg2vxjtpvfn5jjoxevi633xwu
*of*packages with regulatory interactions (dependences and*conflicts*) from Debian GNU/Linux operating system is compiled and used as analogy*of*a gene regulatory network. ... Using a trace-back algorithm we assembly networks from the potential pool*of*packages for both scale-*free*and exponential topology from real and a null model data, respectively. ...*Colours*in the horizontal bars correspond to the number*of*each type*of*package in the null model. Yellow are packages with k con in > 0 or k con out > 0. ...##
###
An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings

2012
*
Computer Science & Engineering An International Journal
*

An optimal algorithm is presented about

doi:10.5121/cseij.2012.2101
fatcat:g66n3ftkunfhtfxde5asul5e2u
*Conflict*-*Free*Coloring for connected subgraphs*of*tree*of*rings. Suppose the number*of*the rings in the tree is |T| and the maximum length*of*rings is |R|. ... A presented algorithm in [1] for a Tree*of*rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors. ... ACKNOWLEDGEMENTS This research has been supported by the business training center*of*tabriz,Iran. ...##
###
Improved lower bounds on parity vertex colourings of binary trees
[article]

2019
*
arXiv
*
pre-print

These lower bounds are also lower bounds for the

arXiv:1910.03341v2
fatcat:op2bgvoa4jbyvp5bvwuvnz2n4u
*conflict*-*free**colouring*. We also prove that χ_p(G) is not monotone with respect to minors and determine its value for cycles. ... A vertex*colouring*is called a parity vertex*colouring*if every path in G contains an odd number*of*occurrences*of*some*colour*. ... The*conflict*-*free**colouring*is a relaxation*of*a unique-maximum*colouring*. ...
« Previous

*Showing results 1 — 15 out of 30,952 results*