EN|RU
English version: Journal of Applied and Industrial Mathematics, 2020, 14:1, 205-211 |
![]() |
Volume 27, No 1, 2020, P. 5-16 UDC 519.175.3
Keywords: enumeration, labeled graph, outerplanar graph, bridgeless graph, $k$-cyclic graph, asymptotics. DOI: 10.33048/daio.2020.27.653 Vitaly A. Voblyi 1 Received March 21, 2019 References[1] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969; Mir, Moscow, 1973).[2] M. Bodirsky and M. Kang, Generating outerplanar graphs uniformly at random, Comb. Probab. Comput. 15 (3), 333–343 (2006). [3] M. Bodirsky, O. Gimenez, M. Kang, and M. Noy, Enumeration and limit laws of series-parallel graphs, Eur. J. Comb. 28 (8), 2091–2105 (2007). [4] M. Drmota, E. Fusy, M. Kang, V. Kraus, and J. Rue, Asymptotic study of subcritical graph classes, SIAM J. Discrete Math. 25 (4), 1615–1651 (2011). [5] V. A. Voblyi, Number of labeled outerplanar $k$-cyclic graphs, Mat. Zametki 103 (5), 657–666 (2018). [6] V. A. Voblyi, A simple formula for the number of labeled outerplanar $k$-cyclic blocks and their asymptotic counting, in Proc. XII Int. Workshop “Discrete Mathematics and Its Applications”, Moscow, Russia, June 20–25, 2016 (Izd. Mekh.-Mat. Fak. Mosk. Gos. Univ., Moscow, 2016), pp. 285–287. [7] P. Hanlon and R. W. Robinson, Counting bridgeless graphs, J. Comb. Theory, Ser. B, 33 (3), 276–305 (1982). [8] V. A. Voblyi, Enumeration of labeled connected graphs with given order and size, Diskretn. Anal. Issled. Oper. 23 (2), 5–20 (2016). [J. Appl. Ind. Math. 10 (2), 302–310 (2016)]. [9] I. P. Goulden and D. M. Jackson, Combinatorial Enumeration (J. Wiley & Sons, New York, 1983; Nauka, Moscow, 1990). [10] V. A. Voblyi, The second Riddell relation and its consequences, Diskretn. Anal. Issled. Oper. 26 (1), 20–32 (2019) [J. Appl. Ind. Math. 13 (1), 168–174 (2019)]. [11] C. McDiarmid and A. Scott, Random graphs from a block stable class, Eur. J. Comb. 58, 96–106 (2016). [12] M. Noy, Random planar graphs and beyond, in Proc. Int. Congr. of Mathematicians, Seoul, Korea, Aug. 13–21, 2014, Vol. IV (ICM 2014 Organ. Comm., Seoul, 2014), pp. 407–431. [13] F. Harary and E. M. Palmer, Graphical Enumeration (Acad. Press, New York, 1973; Mir, Moscow, 1977). [14] V. A. Voblyi, Enumeration of labeled Euler cactuses, in Proc. XI Int. Workshop “Discrete Mathematics and Its Applications”, Moscow, Russia, Jan. 18–23, 2012 (Izd. Mekh.-Mat. Fak. Mosk. Gos. Univ., Moscow, 2012), pp. 275–277. |
|
![]() |
|
© Sobolev Institute of Mathematics, 2015 | |
![]() |
|