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Algorithmic Aspects of Acyclic Edge Colorings

2002
*
Algorithmica
*

A proper

doi:10.1007/s00453-001-0093-8
fatcat:ztckuecsi5amrhyq5t7czjfhg4
*coloring**of*the*edges**of*a graph G is called*acyclic*if there is no 2-*colored*cycle in G. ... Any*acyclic**coloring**of*the*edges**of*F using 3*colors*,*colors*e 1 and e 2 with the same*color*. Proof*of*Lemma 3. ... The*edges**of*F can be*colored**acyclically*using 3*colors*, with no bichromatic path connecting v 1 and v 14 . 2. ...##
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An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

Here we give a quadratic-time

doi:10.1007/978-3-642-21204-8_17
fatcat:bxdyxkl3ivetvm4ilkpc2tvbbu
*algorithm*that finds an*acyclic*4-*edge*-colouring*of*a given connected subcubic graph different from K4 and K3,3. ... An*acyclic**edge*-colouring*of*a graph is a proper*edge*-colouring such that the subgraph induced by the*edges**of*any two colours is*acyclic*. ... The concept*of**acyclic*colourings was introduced by Grünbaum in [11] ; the*algorithmic**aspects**of**acyclic*colourings have recently caught interest because*of*their applications in matrix computations ...##
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Acyclic edge-coloring using entropy compression

2013
*
European journal of combinatorics (Print)
*

An

doi:10.1016/j.ejc.2013.02.007
fatcat:6hrdct6c2jewbpvkhdblhbgjva
*edge*-*coloring**of*a graph G is*acyclic*if it is a proper*edge*-*coloring**of*G and every cycle contains at least three*colors*. ... We prove that every graph with maximum degree Delta has an*acyclic**edge*-*coloring*with at most 4 Delta - 4*colors*, improving the previous bound*of*9.62 (Delta - 1). ... and Zhentao Li for discussions related to*algorithmic*issues. ...##
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Acyclic Edge Coloring through the Lovász Local Lemma
[article]

2018
*
arXiv
*
pre-print

We give a probabilistic analysis

arXiv:1407.5374v9
fatcat:hrrc5rmeqfeaho4rwmhkhkkhsu
*of*a Moser-type*algorithm*for the Lovász Local Lemma (LLL), adjusted to search for*acyclic**edge**colorings**of*a graph. ... Specifically we show that a graph with maximum degree Δ has an*acyclic*proper*edge**coloring*with at most 3.74(Δ-1)+1*colors*, whereas, previously, the best bound was 4(Δ-1). ... We are also much indebted to Gwenaël Joret for pointing out the incompleteness*of*the proof*of*[15, Lemma 5] and for the illuminating for us exchange*of*messages that followed. ...##
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Combinatorial algorithms enabling computational science: tales from the front

2006
*
Journal of Physics, Conference Series
*

The importance

doi:10.1088/1742-6596/46/1/062
fatcat:h3esek46tfdt3pokx6smbpxlcm
*of*discrete*algorithms*continues to grow with the demands*of*new applications and advanced architectures. ... Combinatorial*algorithms*have long played a crucial enabling role in scientific and engineering computations. ... For example, graph*algorithms*have been a key*aspect**of*sparse linear algebra since the 1960s [1] . ...##
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Acyclic edge coloring through the Lovász Local Lemma

2017
*
Theoretical Computer Science
*

We give a probabilistic analysis

doi:10.1016/j.tcs.2016.12.011
fatcat:vza3gse6ivgz5bl2woonk6ftky
*of*a Moser-type*algorithm*for the Lovász Local Lemma (LLL), adjusted to search for*acyclic**edge**colorings**of*a graph. ... Specifically we show that a graph with maximum degree ∆ has an*acyclic*proper*edge**coloring*with at most ⌈3.74(∆ − 1)⌉ + 1*colors*, whereas, previously, the best bound was 4(∆ − 1). ... We are also much indebted to Gwenaël Joret for pointing out the incompleteness*of*the proof*of*[15, Lemma 5] and for the illuminating for us exchange*of*messages that followed. ...##
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Page 8512 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

The

*acyclic**edge*chromatic number*of*G is the least number*of**colors*in an*acyclic**edge**coloring**of*G. ... |Zaks, Ayal] (IL-TLAV-OR; Tel Aviv)*Algorithmic**aspects**of**acyclic**edge**colorings*. (English summary) Algorithmica 32 (2002), no. 4, 611-614. ...##
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ColPack

2013
*
ACM Transactions on Mathematical Software
*

We present a suite

doi:10.1145/2513109.2513110
fatcat:rgsaymoduzh5nd7kqeewhkd53q
*of*fast and effective*algorithms*, encapsulated in a software package called ColPack, for a variety*of*graph*coloring*and related problems. ... Many*of*the*coloring*problems model partitioning needs arising in compression-based computation*of*Jacobian and Hessian matrices using*Algorithmic*Differentiation. ... We thank Fredrik Manne for his comments on an earlier version*of*this paper. ...##
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Acyclic coloring of graphs

1991
*
Random structures & algorithms (Print)
*

In absence

doi:10.1002/rsa.3240020303
fatcat:dq3ainuygfcrnajo2si56jnada
*of*such a bichromatic cycle, an*edge**coloring*is said to be an*acyclic**edge**coloring**of*that graph. ... Similarly, the smallest number*of**colors*required to*acyclically**edge**colors*a graph is called its*acyclic**edge*chromatic number and is denoted by a ′ (G). ... We here note the two important*aspects**of*the nature*of*our*coloring*schemes. 1. ...##
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Two Novel Evolutionary Formulations of the Graph Coloring Problem

2004
*
Journal of combinatorial optimization
*

We introduce two novel evolutionary formulations

doi:10.1023/b:joco.0000021937.26468.b2
fatcat:ywxmgukzibaupj54ph3vgzs6ku
*of*the problem*of**coloring*the nodes*of*a graph. ... It views such orientations as individuals and evolves them with the aid*of*evolutionary operators that are very heavily based on the structure*of*the graph and its*acyclic*orientations. ... Acknowledgments The authors acknowledge partial support from CNPq, CAPES, the PRONEX initiative*of*Brazil's MCT under contract 41.96.0857.00, and a FAPERJ BBP grant. ...##
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Page 72 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

) if some implementa- tion

*of*the*algorithm*uses more*colors*than the chromatic number Similarly, a graph is said to be hard-to-*color*(HC) if every imple- mentation*of*the*algorithm*results in a non-optimal ... The context*of*this problem and its practical*aspects*are given. Further, we indicate how the*algorithm*may be extended for the construction*of*convergent transfer subgraphs.” ...##
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On the Algorithmic Lovász Local Lemma and Acyclic Edge Coloring

2014
*
2015 Proceedings of the Twelfth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
*

Specifically we show that a graph with maximum degree ∆ has an

doi:10.1137/1.9781611973761.2
dblp:conf/analco/0001KPT15
fatcat:jdyqu4jivjbfdp4fsbsdbobsiq
*acyclic*proper*edge**coloring*with at most ⌈3.74(∆ − 1)⌉ + 1*colors*, whereas the previously known best bound was 4(∆ − 1). ... We present an alternative probabilistic analysis*of*the*algorithm*that does not involve reconstructing the history*of*the*algorithm*from the witness tree. ... Rué for showing to us how to deal with the asymptotics*of*the coefficients*of*inverse generating functions. We are grateful to D. Mitsche on one hand and to D. Achlioptas and F. ...##
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Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments

2016
*
Symposium on Theoretical Aspects of Computer Science
*

In particular we show that the vertices

doi:10.4230/lipics.stacs.2016.49
dblp:conf/stacs/KumarL16
fatcat:4mpl7sgm2fhovcjoulgqbnrage
*of*any undirected m-*edge*graph*of*maximum degree d can be*colored*white or black in such a way that for each*of*the two*colors*, the number*of**edges*with both endpoints ...*of*that*color*is between m/4 − d/2 and m/4+d/2. ...*of**edges*with both endpoints*of*that*color*is between m/4 − d/2 and m/4+d/2. ...##
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Fast left-linear semi-unification
[chapter]

1990
*
Lecture Notes in Computer Science
*

We present a generic polynomial-time

doi:10.1007/3-540-53504-7_64
fatcat:jzkgk5ff5rcavclzy4yvho6qla
*algorithm*L1 for LLSU, which shows that LLSU is in P. ... It is the problem*of*solving a set*of*term inequalities M 1 ≤ N 1 , . . . , M k ≤ N k , where ≤ is interpreted as the subsumption preordering on (first-order) terms. ... We show that L1 can be implemented in time O(n 3 ) by using a fast dynamic transitive closure*algorithm*. 3. ...##
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Sequence Hypergraphs
[chapter]

2016
*
Lecture Notes in Computer Science
*

We show that many

doi:10.1007/978-3-662-53536-3_24
fatcat:dmvphzjyvjfs3pioecjn4ggcai
*of*these problems are APX-hard, even in*acyclic*sequence hypergraphs or with hyperedges*of*constant length. ... We introduce sequence hypergraphs by extending the concept*of*a directed*edge*(from simple directed graphs) to hypergraphs. ... We call the set*of*directed*edges*{e i = (v i , v i+1 ) for i = 1, . . . , k − 1} the*edges**of*E. The*edges**of*E are exactly the*edges**of**color*c(E) in the underlying*colored*graph*of*H. ...
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