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Page 2336 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
Summary: “Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number 7(G).  ...  We study uniquely list colorable graphs with a restriction on the number of colors used. In this way, we generalize a theorem which charac- terizes uniquely 2-list colorable graphs.  ... 

On the complexity of some colorful problems parameterized by treewidth

Michael R. Fellows, Fedor V. Fomin, Daniel Lokshtanov, Frances Rosamond, Saket Saurabh, Stefan Szeider, Carsten Thomassen
2011 Information and Computation  
The LIST COLORING problem takes as input a graph G, together with an assignment to each vertex v of a set of colors C v .  ...  The list chromatic number χ l (G) of a graph G is defined to be the smallest positive integer r, such that for every assignment to the vertices v of G, of a list L v of colors, where each list has length  ...  The first author also acknowledges the support provided by a Fellowship to the Institute of Advanced Studies, Durham University, and the support of the Informatics Institute at the University of Bergen  ... 
doi:10.1016/j.ic.2010.11.026 fatcat:sfyj6cofungeplh5riskcy6s5u

Multicoloring trees

Magnús M. Halldórsson, Guy Kortsarz, Andrzej Proskurowski, Ravit Salman, Hadas Shachnai, Jan Arne Telle
2003 Information and Computation  
Scheduling jobs with pairwise conflicts is modeled by the graph multicoloring problem.  ...  We study these versions of the multicoloring problem on trees, under the sum-of-completion-times objective.  ...  We extract the entries of non-descendants of u, augment their values by xðuÞ, and merge the resulting list with L u . This gives the complete list for u.  ... 
doi:10.1016/s0890-5401(02)00032-9 fatcat:4jfprdb7nfc7pe6svjt3wyg2sa

Nonpreemptive Constrained Link Scheduling in Wireless Mesh Networks

Yiqun Wu, Ying Jun Zhang, Zhisheng Niu
2008 IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference  
Our analysis shows that with a randomly selected link-ordering list, throughput degradation of LLS compared to the optimal NPLS is bounded even in the worst case.  ...  This paper considers the problem of link scheduling with non-preemptive constraint in wireless mesh networks.  ...  Let I(t) denote the set of transmitting links at time t. With the conflict graph model, I(t) is an independent set of G c .  ... 
doi:10.1109/glocom.2008.ecp.1010 dblp:conf/globecom/WuZN08 fatcat:gxlphjnn3nc3xias63n4olpwgu

Segmentation and Interpretation of Multicolored Objects with Highlights

Bruce A. Maxwell, Steven A. Shafer
2000 Computer Vision and Image Understanding  
This system is valid for images of piecewise uniform dielectric objects with highlights, moving it beyond the capabilities of previous physics-based segmentation algorithms which assume uniformly colored  ...  The first extension provides interpretations of a scene by reasoning about the likelihood of different physical characteristics of simple image regions.  ...  It is important to note that these compatibility measures are appropriate for the hypotheses listed in the initial hypothesis sets above.  ... 
doi:10.1006/cviu.1999.0801 fatcat:enusspcy3jgdxha7e3xjbzkeqi

XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure [article]

Hans L. Bodlaender and Carla Groenland and Hugo Jacob and Lars Jaffke and Paloma T. Lima
2022 arXiv   pre-print
In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures.  ...  The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set,  ...  q-List-Coloring Input: A graph G = (V, E), a path decomposition of G of width , and lists of available colors among [q] for each vertex of V .  ... 
arXiv:2201.13119v2 fatcat:7ifqqzhjbvcqrpr3lepwbgbwaa

Page 6734 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Paul, MN) g(G) its 20041:05055 05C15 05C85 68R10 68W20 Marx, Daniel (H-BUTE-CIT; Budapest) List edge multicoloring in graphs with few cycles. (English summary) Inform. Process.  ...  Summary: “The list edge multicoloring problem is a version of edge coloring where every edge e has a list of available colors L(e) and an integer demand x(e).  ... 

Incremental List Coloring of Graphs, Parameterized by Conservation [chapter]

Sepp Hartung, Rolf Niedermeier
2010 Lecture Notes in Computer Science  
of the colors specified by its associated list containing some of in total k colors.  ...  Incrementally k-list coloring a graph means that a graph is given by adding stepwise one vertex after another, and for each intermediate step we ask for a vertex coloring such that each vertex has one  ...  Let G = (V, E) with V = {v 1 , . . . , v n } be a k-colored graph (through a coloring f ), taken as an instance for k-Multicolored Independent Set.  ... 
doi:10.1007/978-3-642-13562-0_24 fatcat:lidne5mj5bfkho5kvg7jag76k4

Extending Hall's Theorem into List Colorings: A Partial History

D. G. Hoffman, P. D. Johnson
2007 International Journal of Mathematics and Mathematical Sciences  
New results are presented concerning list colorings of independence systems and colorings of graphs with nonnegative measurable functions on positive measure spaces.  ...  This generalization was formed in the relatively new theory of list colorings of graphs.  ...  For example, in Figure 1 .1 there are two graphs with list assignments indicated (set brackets are omitted).  ... 
doi:10.1155/2007/72168 fatcat:vb5jojohqzc6xgdjey4moy7wby

On Treewidth and Stable Marriage [article]

Sushmita Gupta, Saket Saurabh, Meirav Zehavi
2017 arXiv   pre-print
First, we study the treewidth tw of the primal graph. We establish that all four problems are W[1]-hard.  ...  We thus present a comprehensive, complete picture of the behavior of central optimization versions of Stable Marriage with respect to treewidth.  ...  This concludes the proof of the lemma. In light of Lemma 4.2, the measure δ(µ C SESM ) is well defined. We proceed to analyze this measure with the following lemma. Lemma 4.3.  ... 
arXiv:1707.05404v1 fatcat:wvzfalp4rzd4nn2atrxfzj47j4

On the Complexity of Problems on Tree-structured Graphs [article]

Hans L. Bodlaender and Carla Groenland and Hugo Jacob and Marcin Pilipczuk and Michal Pilipczuk
2022 arXiv   pre-print
Various natural problems on 'tree-structured graphs' are complete for this class: we show that List Coloring and All-or-Nothing Flow parameterized by treewidth are XALP-complete.  ...  Moreover, we introduce 'tree-shaped' variants of Weighted CNF-Satisfiability and Multicolor Clique that are XALP-complete.  ...  Let H be the resulting graph. Now, H has a list coloring, if and only if there is a tree-chained multicolor independent set in G.  ... 
arXiv:2206.11828v1 fatcat:rq2mmd5hgbeadiydafwomuyjuy

List colorings with measurable sets

Jan Hladký, Daniel Kráal, Jean-Sébastien Sereni, Michael Stiebitz
2008 Journal of Graph Theory  
The measurable list chromatic number of a graph G is the smallest number ξ such that if each vertex v of G is assigned a set L(v) of measure ξ in a fixed atomless measure space, then there exist sets c  ...  Graph Theory 54 (2007), 179-193] and show that the measurable list chromatic number of a finite graph G is equal to its fractional chromatic number.  ...  Part of this research was conducted while the first two authors were visiting Georgia Institute of Technology and the middle two authors were visiting Technische Universität Ilmenau.  ... 
doi:10.1002/jgt.20335 fatcat:hxi5nxe6tfglngewheelomo7hy

Strong Colorings of Hypergraphs [chapter]

Geir Agnarsson, Magnús M. Halldórsson
2005 Lecture Notes in Computer Science  
In particular, we give an algebraic scheme using integer programming to color graphs of bounded composition-width.  ...  A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems.  ...  Suppose we are given a graph G with vertex weights w and a Ccoloring of G (i.e., a partition of the vertex set into independent sets).  ... 
doi:10.1007/978-3-540-31833-0_21 fatcat:wpgt4mjnfbaldfxx26dyyssyoe

Finding large H-colorable subgraphs in hereditary graph classes [article]

Maria Chudnovsky, Jason King, Michał Pilipczuk, Paweł Rzążewski, Sophie Spirkl
2020 arXiv   pre-print
in these classes of graphs.  ...  Here, n is the number of vertices of the input graph G and ω(G) is the maximum size of a clique in G.  ...  will be convenient to work with a multicoloring generalization of the problem.  ... 
arXiv:2004.09425v2 fatcat:xjposflbmbafhhgqksipvmw3sm

A cutting plane algorithm for graph coloring

Isabel Méndez-Díaz, Paula Zabala
2008 Discrete Applied Mathematics  
We study the problem from a polyhedral point of view and determine some families of facets of the 0/1-polytope associated with one of these integer programming formulations.  ...  We present an approach based on integer programming formulations of the graph coloring problem. Our goal is to develop models that remove some symmetrical solutions obtained by color permutations.  ...  Independent set inequalities Substructures of a graph give rise to valid inequalities for the coloring polytope of the whole graph.  ... 
doi:10.1016/j.dam.2006.07.010 fatcat:cjq4itu5rjfvzeqczulb547fby
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