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2014 | 34 | 3 | 585-592
Tytuł artykułu

Degree Sequences of Monocore Graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A k-monocore graph is a graph which has its minimum degree and degeneracy both equal to k. Integer sequences that can be the degree sequence of some k-monocore graph are characterized as follows. A nonincreasing sequence of integers d0, . . . , dn is the degree sequence of some k-monocore graph G, 0 ≤ k ≤ n − 1, if and only if k ≤ di ≤ min {n − 1, k + n − i} and ⨊di = 2m, where m satisfies [...] ≤ m ≤ k ・ n − [...] .
Słowa kluczowe
Wydawca
Rocznik
Tom
34
Numer
3
Strony
585-592
Opis fizyczny
Daty
wydano
2014-08-01
otrzymano
2013-01-09
poprawiono
2013-07-09
zaakceptowano
2013-08-08
online
2014-07-16
Twórcy
autor
Bibliografia
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  • [2] J. Alvarez-Hamelin, L. Dall’Asta, A. Barrat, A. Vespignani, k-core decomposition: a tool for the visualization of large scale networks, Adv. Neural Inf. Process. Syst. 18 (2006) 41.
  • [3] G. Bader, C. Hogue, An automated method for finding molecular complexes in large protein interaction networks, BMC Bioinformatics 4 (2003). doi:10.1186/1471-2105-4-2[Crossref][PubMed]
  • [4] V. Batagelj and M. Zaversnik, An O(m) algorithm for cores decomposition of net- works. http://vlado.fmf.uni-lj.si/pub/networks/doc/cores/cores.pdf. (2002) Last accessed November 25, 2011.
  • [5] A. Bickle, The k-cores of a Graph (Ph.D. Dissertation, Western Michigan University, 2010).
  • [6] A. Bickle, Structural results on maximal k-degenerate graphs, Discuss. Math. Graph Theory 32 (2012) 659-676. doi:10.7151/dmgt.1637[Crossref]
  • [7] A. Bickle, Cores and shells of graphs, Math. Bohemica 138 (2013) 43-59.
  • [8] B. Bollobas, Extremal Graph Theory (Academic Press, 1978).
  • [9] M. Borowiecki, J. Ivanˇco, P. Mih´ok and G. Semaniˇsin, Sequences realizable by max- imal k-degenerate graphs, J. Graph Theory 19 (1995) 117-124. doi:10.1002/jgt.3190190112[Crossref]
  • [10] G. Chartrand and L. Lesniak, Graphs and Digraphs, (4th Ed.) (CRC Press, 2005).
  • [11] S. Dorogovtsev, A. Goltsev and J. Mendes, k-core organization of complex networks, Phys. Rev. Lett. 96 (2006).[PubMed][Crossref]
  • [12] Z. Filáková, P. Mihók and G. Semaniˇsin., A note on maximal k-degenerate graphs, Math. Slovaca 47 (1997) 489-498.
  • [13] M. Gaertler and M. Patrignani, Dynamic analysis of the autonomous system graph, Proc. 2nd International Workshop on Inter-Domain Performance and Simulation (2004) 13-24.
  • [14] D.R. Lick and A.T. White, k-degenerate graphs, Canad. J. Math. 22 (1970) 1082-1096. doi:10.4153/CJM-1970-125-1[Crossref]
  • [15] T. Luczak, Size and connectivity of the k-core of a random graph, Discrete Math. 91 (1991) 61-68. doi:10.1016/0012-365X(91)90162-U[Crossref]
  • [16] J. Mitchem, Maximal k-degenerate graphs, Util. Math. 11 (1977) 101-106.
  • [17] S.B. Seidman, Network structure and minimum degree, Soc. Networks 5 (1983) 269-287. doi:10.1016/0378-8733(83)90028-X[Crossref]
  • [18] J.M.S. Simões-Pereira, A survey of k-degenerate graphs, Graph Theory Newsletter 5 (1976) 1-7.
  • [19] D. West, Introduction to Graph Theory, (2nd Ed.) (Prentice Hall, 2001).
  • [20] S. Wuchty and E. Almaas, Peeling the yeast protein network, Proteomics 5 (2005) 444-449. doi:10.1002/pmic.200400962 [Crossref][PubMed]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1759
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