Forcing convexity number of the corona of two graphs

2016 ◽  
Vol 11 ◽  
pp. 667-672
Author(s):  
Lyndon B. Decasa
Keyword(s):  
Convexity Number

Forcing weakly convexity number of a graph

2014 ◽  
Vol 8 ◽  
pp. 4867-4875
Author(s):  
Kezza P. Noguerra ◽  
Sergio R. Canoy, Jr. ◽  
Helen M. Rara ◽  
Elgie T. Liwagon
Keyword(s):  
Convexity Number

scholarly journals On local convexity of nonlinear mappings between Banach spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Iryna Banakh ◽  
Taras Banakh ◽  
Anatolij Plichko ◽  
Anatoliy Prykarpatsky
Keyword(s):  
Banach Space ◽  
Lower Bound ◽  
Banach Spaces ◽  
Lipschitz Constant ◽  
Second Order ◽  
Local Convexity ◽  
Convexity Number ◽  
Locally Convex ◽  
Nonlinear Mappings

AbstractWe find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.

scholarly journals The Forcing Convexity Number of a Graph

2001 ◽  
Vol 51 (4) ◽  
pp. 847-858 ◽  
Author(s):  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Convexity Number

Some Remarks on the Convexity Number of a Graph

2003 ◽  
Vol 19 (3) ◽  
pp. 357-361 ◽  
Author(s):  
John Gimbel
Keyword(s):  
Convexity Number

The Convexity Number of a Graph

2002 ◽  
Vol 18 (2) ◽  
pp. 209-217 ◽  
Author(s):  
Gary Chartrand ◽  
Curtiss E. Wall ◽  
Ping Zhang
Keyword(s):  
Convexity Number

The L1 - Convexity Number of a Graph

2015 ◽  
Vol 5 (2) ◽  
pp. 09
Author(s):  
S. V. Padmavathi ◽  
V. Swaminathan
Keyword(s):  
Convexity Number

2-dimensional Convexity Numbers and P4-free Graphs

2014 ◽  
Vol 57 (1) ◽  
pp. 61-71
Author(s):  
Stefan Geschke
Keyword(s):  
Convex Hull ◽  
Convex Sets ◽  
Element Subset ◽  
Closed Set ◽  
Polish Spaces ◽  
Convex Structure ◽  
Closed Sets ◽  
Convexity Number ◽  
Convex Subsets

AbstractFor S ⊆ ℝn a set C ⊆ S is an m-clique if the convex hull of no m-element subset of C is contained in S. We show that there is essentially just one way to construct a closed set S ⊆ ℝ2 without an uncountable 3-clique that is not the union of countably many convex sets. In particular, all such sets have the same convexity number; that is, they require the same number of convex subsets to cover them. The main result follows from an analysis of the convex structure of closed sets in ℝ2 without uncountable 3-cliques in terms of clopen, P4-free graphs on Polish spaces.

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