Discussiones Mathematicae Graph Theory 28(3) (2008)
511-533
doi: 10.7151/dmgt.1424
Ramin Imany-Nabiyyi
Shahid Beheshti University
Department of Statistics, Evin, Tehran, Iran
e-mail: imany@tabrizu.ac.ir
Keywords: random interval graphs, geometric graphs, geometric probability.
2000 Mathematics Subject Classification: 05C80, 60D05.
[1] | L. Fatto and A.G. Konheim, The random division of an interval and the random covering of a circle, SIAM Review 4 (1962) 211-222, doi: 10.1137/1004058. |
[2] | E. Godehardt and J. Jaworski, On the connectivity of a random interval graphs, Random Structures and Algorithms 9 (1996) 137-161, doi: 10.1002/(SICI)1098-2418(199608/09)9:1/2<137::AID-RSA9>3.0.CO;2-Y. |
[3] | L. Holst and J. Husler, On the random coverage of the circle, J. Appl. Prob. 21 (1984) 558-566, doi: 10.2307/3213617. |
[4] | T. Huillet, Random covering of the circle: the size of the connected components, Adv. in Appl. Probab. 35 (2003) 563-582, doi: 10.1239/aap/1059486818. |
[5] | H. Maehara, On the intersection graph of random arcs on a circle, Random Graphs' 87 (1990) 159-173. |
[6] | M. Penrose, Random Geometric Graphs (Oxford Studies in Probability, 2003), doi: 10.1093/acprof:oso/9780198506263.001.0001. |
[7] | A.F. Siegel, Random arcs on the circle, J. Appl. Prob. 15 (1978) 774-789, doi: 10.2307/3213433. |
[8] | H. Solomon, Geometric Probability (Society for Industrial and Applied Mathematics, Philadelphia, 1976). |
[9] | F.W. Steutel, Random division of an interval, Statistica Neerlandica 21 (1967) 231-244, doi: 10.1111/j.1467-9574.1967.tb00561.x. |
[10] | W.L. Stevens, Solution to a geometrical problem in probability, Ann. Eugenics 9 (1939) 315-320, doi: 10.1111/j.1469-1809.1939.tb02216.x. |
Received 18 February 2008
Revised 4 April 2008
Accepted 7 April 2008