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Asymptotically Good List-Colorings

Jeff Kahn
1996 Journal of combinatorial theory. Series A  
Notice that an ordinary coloring problem in which some colors have already been assigned is a list-coloring problem.  ...  (For instance, if G is an odd cycle and the lists are of size 2, then a coloring exists exactly when not all lists are the same.)  ...  Note A s cannot come from G v , since under K no edge of G v is permanently colored # j .)  ... 
doi:10.1006/jcta.1996.0001 fatcat:un5ilkr5uvdwjevrfqb5zqxe6a

Asymptotics of Hypergraph Matching, Covering and Coloring Problems [chapter]

Jeff Kahn
1995 Proceedings of the International Congress of Mathematicians  
List-colorings and the semirandom method again A rough rationale for the good asymptotics of the types of hypergraphs appearing in Theorems 2.1 and 2.2 is that we are in a probability space -namely M(H  ...  List-colorings The list-chromatic index, x|(W), of H is the least t such that if S (A) is a set ("list") of size t for each A E H, then there exists a coloring a of H with o~(A) G S(A) for each A G H.  ... 
doi:10.1007/978-3-0348-9078-6_130 fatcat:34psrgyyv5amzbilfkjrfykerq

The Irreducible Characters for Semi-Simple Algebraic Groups and for Quantum Groups [chapter]

Henning Haahr Andersen
1995 Proceedings of the International Congress of Mathematicians  
List-colorings and the semirandom method again A rough rationale for the good asymptotics of the types of hypergraphs appearing in Theorems 2.1 and 2.2 is that we are in a probability space -namely M(H  ...  List-colorings The list-chromatic index, x|(W), of H is the least t such that if S (A) is a set ("list") of size t for each A E H, then there exists a coloring a of H with o~(A) G S(A) for each A G H.  ... 
doi:10.1007/978-3-0348-9078-6_66 fatcat:zwbcvzbwibc55igkkponkbd2n4

Some stability and exact results in generalized Turán problems [article]

Dániel Gerbner
2022 arXiv   pre-print
The K k+1 -Turángood graphs listed in Theorem 2.4 are also F -Turán-good.  ...  Now we are ready to list our contributions. Proposition 1.3. Let χ(F ) = k + 1 and H be weakly asymptotically F -Turán-good and weakly K k+1 -Turán-stable. Then H is weakly F -Turán-stable.  ...  In the case H is also K k+1 -Turán-good, we have that the Turán graph maximizes the number of copies of H among complete k-partite n-vertex graphs.  ... 
arXiv:2204.04600v1 fatcat:7jdm5lhgwbcifmyt5mghxqh2fm

Page 3812 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
asymptotically good?”  ...  Mark (1-MT; Missoula, MT) Asymptotically good choice numbers of multigraphs. (English summary) Ars Combin. 60 (2001), 209-217.  ... 

Page 27 of The Trend in Engineering Vol. 6, Issue 2 [page]

1954 The Trend in Engineering  
Cal- culated deflections, based on asymptotic approxima- tion to the exact non-linear differential equation of bending, are shown to be in good agreement with experimental data.  ...  Two types of end connections were used: a top-and-seat-angle arrangement and a web-angle connection similar to the standard beam connections listed in the AISC Manual.  ... 

Locality-Aware Dynamic Task Graph Scheduling

Jordyn Maglalang, Sriram Krishnamoorthy, Kunal Agrawal
2017 2017 46th International Conference on Parallel Processing (ICPP)  
predecessors //List of predecessors' keys 4 List successors //List of successor nodes 5 virtual void init() //initialize this code (user−defined) 6 virtual void compute() //compute this task representing  ...  this node (user−defined) 7 int color() = color(node.key) //helper function: this node's color 9 int color(Key key) //user−defined function mapping a key to its color  ...  This function is called on a list of colors colors (and implicitly, a set of nodes which have these colors).  ... 
doi:10.1109/icpp.2017.16 dblp:conf/icpp/MaglalangKA17 fatcat:mckiduh6j5fupifqggdds35frq

Maximum Average Degree and Vizing's Conjecture [article]

Joshua Harrelson, Hannah Reavis
2022 arXiv   pre-print
When Δ≤20 the value of m is close to 1/2Δ, but as Δ increases m becomes asymptotic to about 1/4Δ+5.  ...  For a graph G and nonnegative integer k, we say G is a k-list-edge-critical graph if χ'_ℓ(G)>k, but χ'_ℓ(G-e)≤ k for all e ∈ E(G).  ...  In this sense, good counts are achieved from knowing the list-edge-colorability of bipartite graphs.  ... 
arXiv:2207.03869v1 fatcat:742bxrcutzhefngftj372xkw4y

Asymptotic differential approximation ratio: Definitions, motivations and application to some combinatorial problems

Marc Demange, Vangelis Th. Paschos
1999 Reserche operationelle  
We show in this section how the notion of asymptotic differential approximation ratio provides a framework in which Algorithm 1 can be also analyzed with good results.  ...  List L is divided into two sub-lists L of cardinality m, and L 1 of cardinality m', with L= \xi e L :xi < L' = L\L.  ... 
doi:10.1051/ro:1999121 fatcat:qnz2tvukqvf7fcdzafc2crurye

Page 7557 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Mark (1-MT; Missoula, MT) Asymptotically good colourings of graphs and multigraphs.  ...  Summary: “A multigraph invariant / admitting formulation as the solution to an integer program is asymptotically good, or a.g., in the case in which £/f* — | as B* — o6 (f* is the solution of the linear  ... 

The channel assignment problem for mutually adjacent sites

Jerrold R Griggs, Daphne Der-Fen Liu
1994 Journal of combinatorial theory. Series A  
It was shown by Rabinowitz and Proulx that the asymptotic coloring efficiency rt(T):= limn~=(n/% ,) exists for every set T.  ...  A T-coloring Let c% denote the optimal span of the T-colorings f of the complete graph Kn, that is, % = minf{max",. ~ vlf(u) -f(v)]}.  ...  asymptotically in optimal T-colorings of Kn.  ... 
doi:10.1016/0097-3165(94)90096-5 fatcat:gkua6wtlmra35grj6m2cfbiwci

The minimum number of edges in a 4-critical graph that is bipartite plus 3 edges

A.V. Kostochka, B.M. Reiniger
2015 European journal of combinatorics (Print)  
List coloring Define a restricted type of coloring as follows. Given a graph G , a list assignment L assigns to each v ∈ V (G ) a set of colors L(v ).  ...  G is L-colorable if there is a proper coloring φ such that for every v , φ(v ) ∈ L(v ). G is k-choosable if G is L-colorable for every list assignment L with |L(v )| ≥ k for all v .  ... 
doi:10.1016/j.ejc.2014.12.002 fatcat:uzfyvd3zp5hw5e25q76u7hbtm4

Continued Fractions and the 4-Color Theorem [article]

Richard Evan Schwartz
2022 arXiv   pre-print
We also present a conjectural sharp "isoperimetric inequality" for colorings of this kind of triangulation.  ...  We study the geometry of some proper 4-colorings of the vertices of sphere triangulations with degree sequence 6,...,6,2,2,2.  ...  In any good coloring, if we can find a vertex of degree 6 where the colors alternate, we can switch the colors and get another good coloring.  ... 
arXiv:2208.05254v1 fatcat:sp75jrv37na7henp5jfzec2mwm

Observation of color-transparency in diffractive dissociation of pions [article]

E791 Collaboration, E.M. Aitala, et al
2000 arXiv   pre-print
These values are in agreement with those predicted by theoretical calculations of color-transparency.  ...  Extrapolating to asymptotically high energies (where t_min approaches 0) we find that when the per-nucleus cross-section for this process is parameterized as σ = σ_0 A^α, α has values near 1.6, the exact  ...  We extrapolate our calculations of α to asymptotically high energies dividing the yields by these factors. The results for each k t bin are listed in Table I .  ... 
arXiv:hep-ex/0010044v1 fatcat:jgxoxlvsmjekjhyltgz7smszqa

Is rapid automatized naming automatic?

George K. Georgiou, Blair Stewart
2013 Preschool and Primary Education  
Twenty-five good readers and twenty-five poor readers were assessed on RAN Colors and Digits and their sound files were analyzed.  ...  No asymptote was reached for color and object naming even among the group of adults (36-65 years old).  ...  The children were given a list of 104 words, divided into four columns of 26 words each, and asked to read them as fast as possible. A short, 8-word practice list was presented first.  ... 
doi:10.12681/ppej.46 fatcat:3gprlugkrbfnjam2rk6wwpq3iy
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