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2011 | 31 | 4 | 753-761
Tytuł artykułu

Spanning tree congestion of rook's graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T - e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Kₘ ☐ Kₙ for any m and n.
Słowa kluczowe
Wydawca
Rocznik
Tom
31
Numer
4
Strony
753-761
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-08-03
poprawiono
2010-11-15
zaakceptowano
2010-11-15
Twórcy
  • Electric Power Development Co., Ltd., 6-15-1, Ginza, Chuo-ku, Tokyo, 104-8165, Japan
autor
  • Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Bibliografia
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  • [3] S.L. Bezrukov, Edge isoperimetric problems on graphs, in: L. Lovasz, A. Gyarfas, G.O.H. Katona, A. Recski and L. Szekely, eds, Graph Theory and Combinatorial Biology, 7 Bolyai Soc. Math. Stud. 157-197 Janos Bolyai Math. Soc. (Budapest, 1999).
  • [4] H.L. Bodlaender, K. Kozawa, T. Matsushima and Y. Otachi, Spanning Tree Congestion of k-outerplanar Graphs, in: WAAC 2010 (2010) 34-39.
  • [5] A. Castejón and M.I. Ostrovskii, Minimum congestion spanning trees of grids and discrete toruses, Discuss. Math. Graph Theory 29 (2009) 511-519, doi: 10.7151/dmgt.1461.
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  • [9] K. Kozawa and Y. Otachi and K. Yamazaki, On spanning tree congestion of graphs, Discrete Math. 309 (2009) 4215-4224, doi: 10.1016/j.disc.2008.12.021.
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  • [11] R. Laskar and C. Wallis, Chessboard graphs, related designs, and domination parameters, J. Statist. Plann. Inference 76 (1999) 285-294, doi: 10.1016/S0378-3758(98)00132-3.
  • [12] H.-F. Law, Spanning tree congestion of the hypercube, Discrete Math. 309 (2009) 6644-6648, doi: 10.1016/j.disc.2009.07.007.
  • [13] J.H. Lindsey II, Assignment of numbers to vertices, Amer. Math. Monthly 71 (1964) 508-516, doi: 10.2307/2312587.
  • [14] J.W. Moon, On the Line-Graph of the Complete Bigraph, Ann. Math. Statist. 34 (1963) 664-667, doi: 10.1214/aoms/1177704179.
  • [15] M.I. Ostrovskii, Minimum congestion spanning trees in planar graphs, Discrete Math. 310 (2010) 1204-1209, doi: 10.1016/j.disc.2009.11.016.
  • [16] M.I. Ostrovskii, Minimal congestion trees, Discrete Math. 285 (2004) 219-226, doi: 10.1016/j.disc.2004.02.009.
  • [17] Y. Otachi, H.L. Bodlaender and E.J. van Leeuwen, Complexity Results for the Spanning Tree Congestion Problem, in: WG 2010, 6410 Lecture Notes in Comput. Sci. (Springer-Verlag, 2010) 3-14.
  • [18] S. Simonson, A variation on the min cut linear arrangement problem, Math. Syst. Theory 20 (1987) 235-252, doi: 10.1007/BF01692067.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1577
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