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41st Annual Symposium on Foundations of Computer Science
Universality and tolerance
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
N. Alon, M. Capalbo, Y. Kohayakawa, V. Rodl, A. Rucinski, E. Szemeredi, "Universality and tolerance," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 14, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892007, author = {N. Alon and M. Capalbo and Y. Kohayakawa and V. Rodl and A. Rucinski and E. Szemeredi}, title = {Universality and tolerance}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {14}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892007}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Universality and tolerance SN  02725428 SP EP A1  N. Alon, A1  M. Capalbo, A1  Y. Kohayakawa, A1  V. Rodl, A1  A. Rucinski, A1  E. Szemeredi, PY  2000 KW  graph theory; graph theory; universality; tolerance; positive integers; graphs; vertices; bipartite graphs; maximum degree; sparse universal graphs; random constructions; faulttolerant bipartite random graph VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
For any positive integers r and n, let H(r,n) denote the family of graphs on n vertices with maximum degree r, and let H(r,n,n) denote the family of bipartite graphs H on 2n vertices with n vertices in each vertex class, and with maximum degree r. On one hand, we note that any H(r,n)universal graph must have /spl Omega/(n/sup 22/r/) edges. On the other hand, for any n/spl ges/n/sub 0/(r), we explicitly construct H(r,n)universal graphs G and /spl Lambda/ on n and 2n vertices, and with O(n/sup 2/spl Omega//(1/r log r)) and O(n/sup 21/r/ log/sup 1/r/ n) edges, respectively, such that we can efficiently find a copy of any H /spl epsiv/ H (r,n) in G deterministically. We also achieve sparse universal graphs using random constructions. Finally, we show that the bipartite random graph G=G(n,n,p), with p=cn/sup 1/2r/ log/sup 1/2r/ n is faulttolerant; for a large enough constant c, even after deleting any /spl alpha/fraction of the edges of G, the resulting graph is still H(r,/spl alpha/(/spl alpha/)n,/spl alpha/(/spl alpha/)n)universal for some /spl alpha/: [0,1)/spl rarr/(0,1].
Index Terms:
graph theory; graph theory; universality; tolerance; positive integers; graphs; vertices; bipartite graphs; maximum degree; sparse universal graphs; random constructions; faulttolerant bipartite random graph
Citation:
N. Alon, M. Capalbo, Y. Kohayakawa, V. Rodl, A. Rucinski, E. Szemeredi, "Universality and tolerance," focs, pp.14, 41st Annual Symposium on Foundations of Computer Science, 2000
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