Filters








7,024 Hits in 5.4 sec

Algorithmic Aspects of Acyclic Edge Colorings

Alon, Zaks
2002 Algorithmica  
A proper 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.  ... 
doi:10.1007/s00453-001-0093-8 fatcat:ztckuecsi5amrhyq5t7czjfhg4

An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs [chapter]

Edita Máčajová, Ján Mazák
2011 Lecture Notes in Computer Science  
Here we give a quadratic-time 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  ... 
doi:10.1007/978-3-642-21204-8_17 fatcat:bxdyxkl3ivetvm4ilkpc2tvbbu

Acyclic edge-coloring using entropy compression

Louis Esperet, Aline Parreau
2013 European journal of combinatorics (Print)  
An 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.  ... 
doi:10.1016/j.ejc.2013.02.007 fatcat:6hrdct6c2jewbpvkhdblhbgjva

Acyclic Edge Coloring through the Lovász Local Lemma [article]

Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, and Dimitrios M. Thilikos
2018 arXiv   pre-print
We give a probabilistic analysis 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.  ... 
arXiv:1407.5374v9 fatcat:hrrc5rmeqfeaho4rwmhkhkkhsu

Combinatorial algorithms enabling computational science: tales from the front

Sanjukta Bhowmick, Erik G Boman, Karen Devine, Assefaw Gebremedhin, Bruce Hendrickson, Paul Hovland, Todd Munson, Alex Pothen
2006 Journal of Physics, Conference Series  
The importance 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] .  ... 
doi:10.1088/1742-6596/46/1/062 fatcat:h3esek46tfdt3pokx6smbpxlcm

Acyclic edge coloring through the Lovász Local Lemma

Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, Dimitrios M. Thilikos
2017 Theoretical Computer Science  
We give a probabilistic analysis 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.  ... 
doi:10.1016/j.tcs.2016.12.011 fatcat:vza3gse6ivgz5bl2woonk6ftky

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.  ... 

ColPack

Assefaw H. Gebremedhin, Duc Nguyen, Md. Mostofa Ali Patwary, Alex Pothen
2013 ACM Transactions on Mathematical Software  
We present a suite 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.  ... 
doi:10.1145/2513109.2513110 fatcat:rgsaymoduzh5nd7kqeewhkd53q

Acyclic coloring of graphs

Noga Alon, Colin Mcdiarmid, Bruce Reed
1991 Random structures & algorithms (Print)  
In absence 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.  ... 
doi:10.1002/rsa.3240020303 fatcat:dq3ainuygfcrnajo2si56jnada

Two Novel Evolutionary Formulations of the Graph Coloring Problem

Valmir C. Barbosa, Carlos A.G. Assis, Josina O. Do Nascimento
2004 Journal of combinatorial optimization  
We introduce two novel evolutionary formulations 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.  ... 
doi:10.1023/b:joco.0000021937.26468.b2 fatcat:ywxmgukzibaupj54ph3vgzs6ku

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.”  ... 

On the Algorithmic Lovász Local Lemma and Acyclic Edge Coloring

Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, Dimitrios M. Thilikos
2014 2015 Proceedings of the Twelfth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
Specifically we show that a graph with maximum degree ∆ has an 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.  ... 
doi:10.1137/1.9781611973761.2 dblp:conf/analco/0001KPT15 fatcat:jdyqu4jivjbfdp4fsbsdbobsiq

Faster Exact and Parameterized Algorithm for Feedback Vertex Set in Tournaments

Mithilesh Kumar, Daniel Lokshtanov, Marc Herbstritt
2016 Symposium on Theoretical Aspects of Computer Science  
In particular we show that the vertices 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.  ... 
doi:10.4230/lipics.stacs.2016.49 dblp:conf/stacs/KumarL16 fatcat:4mpl7sgm2fhovcjoulgqbnrage

Fast left-linear semi-unification [chapter]

Fritz Henglein
1990 Lecture Notes in Computer Science  
We present a generic polynomial-time 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.  ... 
doi:10.1007/3-540-53504-7_64 fatcat:jzkgk5ff5rcavclzy4yvho6qla

Sequence Hypergraphs [chapter]

Kateřina Böhmová, Jérémie Chalopin, Matúš Mihalák, Guido Proietti, Peter Widmayer
2016 Lecture Notes in Computer Science  
We show that many 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.  ... 
doi:10.1007/978-3-662-53536-3_24 fatcat:dmvphzjyvjfs3pioecjn4ggcai
« Previous Showing results 1 — 15 out of 7,024 results