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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*. ...##
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On the complexity of some colorful problems parameterized by treewidth

2011
*
Information and Computation
*

The

doi:10.1016/j.ic.2010.11.026
fatcat:sfyj6cofungeplh5riskcy6s5u
*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 ...##
###
Multicoloring trees

2003
*
Information and Computation
*

Scheduling jobs

doi:10.1016/s0890-5401(02)00032-9
fatcat:4jfprdb7nfc7pe6svjt3wyg2sa
*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. ...##
###
Nonpreemptive Constrained Link Scheduling in Wireless Mesh Networks

2008
*
IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference
*

Our analysis shows that

doi:10.1109/glocom.2008.ecp.1010
dblp:conf/globecom/WuZN08
fatcat:gxlphjnn3nc3xias63n4olpwgu
*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 . ...##
###
Segmentation and Interpretation of Multicolored Objects with Highlights

2000
*
Computer Vision and Image Understanding
*

This system is valid for images

doi:10.1006/cviu.1999.0801
fatcat:enusspcy3jgdxha7e3xjbzkeqi
*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. ...##
###
XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure
[article]

2022
*
arXiv
*
pre-print

In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width

arXiv:2201.13119v2
fatcat:7ifqqzhjbvcqrpr3lepwbgbwaa
*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 . ...##
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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]

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*. ...

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

2007
*
International Journal of Mathematics and Mathematical Sciences
*

New results are presented concerning

doi:10.1155/2007/72168
fatcat:vb5jojohqzc6xgdjey4moy7wby
*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). ...##
###
On Treewidth and Stable Marriage
[article]

2017
*
arXiv
*
pre-print

First, we study the treewidth tw

arXiv:1707.05404v1
fatcat:wvzfalp4rzd4nn2atrxfzj47j4
*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. ...##
###
On the Complexity of Problems on Tree-structured Graphs
[article]

2022
*
arXiv
*
pre-print

Various natural problems on 'tree-structured

arXiv:2206.11828v1
fatcat:rq2mmd5hgbeadiydafwomuyjuy
*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. ...##
###
List colorings with measurable sets

2008
*
Journal of Graph Theory
*

The

doi:10.1002/jgt.20335
fatcat:hxi5nxe6tfglngewheelomo7hy
*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. ...##
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Strong Colorings of Hypergraphs
[chapter]

2005
*
Lecture Notes in Computer Science
*

In particular, we give an algebraic scheme using integer programming to color

doi:10.1007/978-3-540-31833-0_21
fatcat:wpgt4mjnfbaldfxx26dyyssyoe
*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*). ...##
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Finding large H-colorable subgraphs in hereditary graph classes
[article]

2020
*
arXiv
*
pre-print

in these classes

arXiv:2004.09425v2
fatcat:xjposflbmbafhhgqksipvmw3sm
*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. ...##
###
A cutting plane algorithm for graph coloring

2008
*
Discrete Applied Mathematics
*

We study the problem from a polyhedral point

doi:10.1016/j.dam.2006.07.010
fatcat:cjq4itu5rjfvzeqczulb547fby
*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*. ...
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