On the chromatic vertex stability number of graphs

A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830915500500 ◽

2015 ◽

Vol 07 (04) ◽

pp. 1550050

Author(s):

Carlos J. Luz

Keyword(s):

Quadratic Programming ◽

Discrete Math ◽

Convex Quadratic Programming ◽

Stability Number ◽

Weighted Version ◽

Similar Characterization ◽

Number Formula ◽

Weighted Stability ◽

Theta Number

For any graph [Formula: see text] Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math. 19(2) (2005) 382–387] introduced a characterization of the Lovász number [Formula: see text] based on convex quadratic programming. A similar characterization is now established for the weighted version of the number [Formula: see text] independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci. 3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory 25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of [Formula: see text] coincides with the weighted stability number is characterized.

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A Branch and Bound Algorithm for the Stability Number of a Sparse Graph

INFORMS Journal on Computing ◽

10.1287/ijoc.10.4.438 ◽

1998 ◽

Vol 10 (4) ◽

pp. 438-447 ◽

Cited By ~ 27

Author(s):

E. C. Sewell

Keyword(s):

Branch And Bound ◽

Branch And Bound Algorithm ◽

Sparse Graph ◽

Stability Number ◽

The Stability

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STABILITY OF HIGH DENSITY CUBES IN RUBBLE MOUND BREAKWATERS

Coastal Engineering Proceedings ◽

10.9753/icce.v36v.structures.4 ◽

2020 ◽

pp. 4

Author(s):

Yalcin Yuksel ◽

Marcel van Gent ◽

Esin Cevik ◽

H. Alper Kaya ◽

Irem Gumuscu ◽

...

Keyword(s):

Relative Density ◽

Slope Angle ◽

High Density ◽

Experimental Results ◽

Normal Density ◽

Stability Number ◽

Damage Initiation ◽

Rubble Mound ◽

The Stability ◽

Rubble Mound Breakwaters

The stability number for rubble mound breakwaters is a function of several parameters and depends on unit shape, placing method, slope angle, relative density, etc. In this study two different densities for cubes in breakwater armour layers were tested to determine the influence of the density on the stability. The experimental results show that the stability of high density blocks were found to be more stable and the damage initiation for high density blocks started at higher stability numbers compared to normal density cubes.

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