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August  2016, 10(3): 541-545. doi: 10.3934/amc.2016024

A note on Erdős-Ko-Rado sets of generators in Hermitian polar spaces

Klaus Metsch 1,

1. 

Justus-Liebig-Universität, Mathematisches Institut, Arndtstraβe 2, D-35392 Gieβen, Belgium

Received  May 2015 Revised  July 2015 Published  August 2016

The size of the largest Erdős-Ko-Rado set of generators in a finite classical polar space is known for all polar spaces except for $H(2d-1,q^2)$ when $d\ge 5$ is odd. We improve the known upper bound in this remaining case by using a variant of the famous Hoffman's bound.
Keywords: Polar space, Erdős-Ko-Rado set..
Mathematics Subject Classification: Primary: 05B25, 05E30, 51A5.
Citation: Klaus Metsch. A note on Erdős-Ko-Rado sets of generators in Hermitian polar spaces. Advances in Mathematics of Communications, 2016, 10 (3) : 541-545. doi: 10.3934/amc.2016024
References:
[1]

A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-regular graphs, in Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, 1989. doi: 10.1007/978-3-642-74341-2.  Google Scholar

[2]

R. J. Elzinga and D. A. Gregory, Weighted matrix eigenvalue bounds on the independence number of a graph, Electr. J. Linear Algebra, 20 (2010), 468-489. doi: 10.13001/1081-3810.1388.  Google Scholar

[3]

C. D. Godsil and M. W. Newman, Eigenvalue bounds for independent sets, J. Combin. Theory Ser. B, 98 (2008), 721-734. doi: 10.1016/j.jctb.2007.10.007.  Google Scholar

[4]

F. Ihringer and K. Metsch, On the maximum size of Erdős-Ko-Rado sets in $H(2d+1, q^2)$, Des. Codes Cryptogr., 72 (2014), 311-316. doi: 10.1007/s10623-012-9765-4.  Google Scholar

[5]

C. J. Luz, A characterization of Delsarte's linear programming bound as a ratio bound, Linear Algebra Appl., 423 (2007), 99-108. doi: 10.1016/j.laa.2006.10.009.  Google Scholar

[6]

K. Metsch, An Erdős-Ko-Rado theorem for finite classical polar spaces,, J. Algebraic Combin., ().  doi: 10.1007/s10801-015-0637-7.  Google Scholar

[7]

V. Pepe, L. Storme and F. Vanhove, Theorems of Erdős-Ko-Rado type in polar spaces, J. Combin. Theory Ser. A, 118 (2011), 1291-1312. doi: 10.1016/j.jcta.2011.01.003.  Google Scholar

[8]

F. Vanhove, Incidence Geometry from an Algebraic Graph Theory Point of View, Ph.D thesis, Univ. Gent, Belgium, 2011. Google Scholar

show all references

References:
[1]

A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-regular graphs, in Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, 1989. doi: 10.1007/978-3-642-74341-2.  Google Scholar

[2]

R. J. Elzinga and D. A. Gregory, Weighted matrix eigenvalue bounds on the independence number of a graph, Electr. J. Linear Algebra, 20 (2010), 468-489. doi: 10.13001/1081-3810.1388.  Google Scholar

[3]

C. D. Godsil and M. W. Newman, Eigenvalue bounds for independent sets, J. Combin. Theory Ser. B, 98 (2008), 721-734. doi: 10.1016/j.jctb.2007.10.007.  Google Scholar

[4]

F. Ihringer and K. Metsch, On the maximum size of Erdős-Ko-Rado sets in $H(2d+1, q^2)$, Des. Codes Cryptogr., 72 (2014), 311-316. doi: 10.1007/s10623-012-9765-4.  Google Scholar

[5]

C. J. Luz, A characterization of Delsarte's linear programming bound as a ratio bound, Linear Algebra Appl., 423 (2007), 99-108. doi: 10.1016/j.laa.2006.10.009.  Google Scholar

[6]

K. Metsch, An Erdős-Ko-Rado theorem for finite classical polar spaces,, J. Algebraic Combin., ().  doi: 10.1007/s10801-015-0637-7.  Google Scholar

[7]

V. Pepe, L. Storme and F. Vanhove, Theorems of Erdős-Ko-Rado type in polar spaces, J. Combin. Theory Ser. A, 118 (2011), 1291-1312. doi: 10.1016/j.jcta.2011.01.003.  Google Scholar

[8]

F. Vanhove, Incidence Geometry from an Algebraic Graph Theory Point of View, Ph.D thesis, Univ. Gent, Belgium, 2011. Google Scholar

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