2005
DOI: 10.1002/jgt.20113
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Nordhaus–Gaddum‐type Theorems for decompositions into many parts

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Cited by 16 publications
(11 citation statements)
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“…Moreover, it is known that (2; K n ) = (2; K n ) = (2; K n ) = (2; K n ) = n + 1. For a short proof, see [9]. This paper deals mainly with decompositions of the complete graph K n and establishes lower and upper bounds for p(k; K n ) where p ∈ { , , , }.…”
Section: Motivation and Main Resultsmentioning
confidence: 98%
See 1 more Smart Citation
“…Moreover, it is known that (2; K n ) = (2; K n ) = (2; K n ) = (2; K n ) = n + 1. For a short proof, see [9]. This paper deals mainly with decompositions of the complete graph K n and establishes lower and upper bounds for p(k; K n ) where p ∈ { , , , }.…”
Section: Motivation and Main Resultsmentioning
confidence: 98%
“…In [9] the following two theorems were proved. The first result establishes a lower bound on (k; ) that is approximately (7k + 24gk + k 2 )/2.…”
Section: (G) (G) (G) (G) H (G)mentioning
confidence: 91%
“…Watkinson [15] improved the upper bound to χ k (K n ) ≤ n + k! 2 and Füredi et al [5] to χ k (K n ) ≤ n + 7 k . Regarding the graphs with bounded genus, let us define χ k (S) to be the maximum of χ k (G) over all graphs G that can be embedded in the surface S. Stiebitz anď Skrekovski [14] have determined the exact values of χ 2 for all surfaces.…”
Section: Introduction and Definitionsmentioning
confidence: 96%
“…Regarding the graphs with bounded genus, let us define χ k (S) to be the maximum of χ k (G) over all graphs G that can be embedded in the surface S. Stiebitz anď Skrekovski [14] have determined the exact values of χ 2 for all surfaces. Füredi et al [5] have shown that…”
Section: Introduction and Definitionsmentioning
confidence: 98%
“…We extend the problem for multicolorings as well and prove asymptotic results for infinitely many cases. We also show that the smallest order of C 4 -free bipartite graphs with χ FF (G) = k is asymptotically 2k 2 (the upper bound answers a problem of Zaker [9]). © 2008 Wiley Periodicals, Inc. J Graph Theory 59: [75][76][77][78][79][80][81][82][83][84][85][86][87][88]2008 Keywords: graphs; chromatic number; greedy algorithm; difference set; projective planes; quadrilateral-free 2000 Mathematics Subject Classification: 05C15, 05C35…”
mentioning
confidence: 98%