scholarly journals The rainbow vertex-index of complementary graphs

2015 ◽  
Vol 2 (3) ◽  
Author(s):  
Fengnan Yanling ◽  
Zhao Wang ◽  
Chengfu Ye ◽  
Shumin Zhang
Keyword(s):  
Vertex Index

scholarly journals Random approximation and the vertex index of convex bodies

2016 ◽  
Vol 108 (2) ◽  
pp. 209-221 ◽  
Author(s):  
Silouanos Brazitikos ◽  
Giorgos Chasapis ◽  
Labrini Hioni
Keyword(s):  
Convex Bodies ◽  
Vertex Index

Use of Vertex Index in Structure-Activity Analysis and Design of Molecules

2012 ◽  
Vol 8 (2) ◽  
pp. 128-134 ◽  
Author(s):  
Chandan Raychaudhury ◽  
Debnath Pal
Keyword(s):  
Activity Analysis ◽  
Analysis And Design ◽  
Structure Activity ◽  
Vertex Index

A Remark on Vertex Index of the Convex Bodies

2012 ◽  
pp. 255-265 ◽  
Author(s):  
Efim D. Gluskin ◽  
Alexander E. Litvak
Keyword(s):  
Convex Bodies ◽  
Vertex Index

Asymmetry of Convex Polytopes and Vertex Index of Symmetric Convex Bodies

2008 ◽  
Vol 40 (4) ◽  
pp. 528-536 ◽  
Author(s):  
E. D. Gluskin ◽  
A. E. Litvak
Keyword(s):  
Convex Polytopes ◽  
Convex Bodies ◽  
Symmetric Convex ◽  
Vertex Index

scholarly journals On the vertex index of convex bodies

2007 ◽  
Vol 215 (2) ◽  
pp. 626-641 ◽  
Author(s):  
K. Bezdek ◽  
A.E. Litvak
Keyword(s):  
Convex Bodies ◽  
Vertex Index

Volume ratios for Cartesian products of convex bodies

2021 ◽  
Vol 32 (5) ◽  
pp. 905-916
Author(s):  
A. Khrabrov
Keyword(s):  
Convex Bodies ◽  
Volume Ratio ◽  
Symmetric Convex ◽  
Partial Differential ◽  
Cartesian Products ◽  
Content Type ◽  
Vertex Index

The paper is devoted to the behavior of volume ratios, the modified Banach–Mazur distance, and the vertex index for sums of convex bodies. It is shown that sup d ( A ⊕ K , B ⊕ L ) ≥ sup ∂ ( A ⊕ K , B ⊕ L ) ≥ c ⋅ n 1 − k + k ′ 2 n , \begin{equation*} \sup d (\mathrm {A}\oplus \mathrm {K},\mathrm {B}\oplus \mathrm {L}) \geq \sup \partial (\mathrm {A}\oplus \mathrm {K},\mathrm {B}\oplus \mathrm {L}) \geq c \cdot n^{1-\frac {k+k’}{2n}}, \end{equation*} if K ⊂ R n \mathrm {K}\subset \mathbb {R}^n and L ⊂ R k \mathrm {L}\subset \mathbb {R}^k are convex and symmetric (the supremum is taken over all symmetric convex bodies A ⊂ R n − k \mathrm {A}\subset \mathbb {R}^{n-k} and B ⊂ R n − k ′ ) \mathrm {B}\subset \mathbb {R}^{n-k’}) . Furthermore, some examples are discussed that show that the available extimates of the vertex index in terms of the volume ratio are not sharp.

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