On graph thickness, geometric thickness, and separator theorems
Tài liệu tham khảo
Kainen, 1973, Thickness and coarseness of graphs, Abh. Math. Sem. Univ. Hamburg, 39, 88, 10.1007/BF02992822
Halton, 1991, On the thickness of graphs of given degree, Inform. Sci., 54, 219, 10.1016/0020-0255(91)90052-V
Pach, 2001, Embedding planar graphs at fixed vertex locations, Graphs Combin., 17, 717, 10.1007/PL00007258
Harary, 1961, Research problem, Bull. Amer. Math. Soc., 67, 542, 10.1090/S0002-9904-1961-10677-0
Battle, 1962, Every planar graph with nine points has a nonplanar complement, Bull. Amer. Math. Soc., 68, 569, 10.1090/S0002-9904-1962-10850-7
Tutte, 1963, The non-biplanar character of the complete 9-graph, Canad. Math. Bull., 6, 319, 10.4153/CMB-1963-026-x
Tutte, 1963, The thickness of a graph, Indag. Math., 25, 567, 10.1016/S1385-7258(63)50055-9
Mutzel, 1998, The thickness of graphs: A survey, Graphs Combin., 14, 59, 10.1007/PL00007219
Dillencourt, 2000, Geometric thickness of complete graphs, J. Graph Algorithms Appl., 4, 5, 10.7155/jgaa.00023
Bernhart, 1979, The book thickness of a graph, J. Combin. Theory Ser. B, 27, 320, 10.1016/0095-8956(79)90021-2
Eppstein
Eppstein, 2004, Separating thickness from geometric thickness, vol. 342, 75
Nash-Williams, 1961, Edge-disjoint spanning trees of finite graphs, J. Lond. Math. Soc., 36, 445, 10.1112/jlms/s1-36.1.445
Nash-Williams, 1964, Decomposition of finite graphs into forests, J. Lond. Math. Soc., 39, 12, 10.1112/jlms/s1-39.1.12
Tutte, 1961, On the problem of decomposing a graph into n connected factors, J. Lond. Math. Soc., 36, 221, 10.1112/jlms/s1-36.1.221
Akiyama, 1981, Covering and packing in graphs. IV. Linear arboricity, Networks, 11, 69, 10.1002/net.3230110108
Alon, 1988, The linear arboricity of graphs, Israel J. Math., 62, 311, 10.1007/BF02783300
Guy, 1990, The outerthickness & outercoarseness of graphs. I. The complete graph & the n-cube, 297
Guy, 1990, The outerthickness & outercoarseness of graphs. II. The complete bipartite graph, 313
Aggarwal, 1991, Multilayer grid embeddings for VLSI, Algorithmica, 6, 129, 10.1007/BF01759038
Brass, 2007, On simultaneous planar graph embeddings, Comput. Geom.: Theory Appl., 36, 117, 10.1016/j.comgeo.2006.05.006
Duncan, 2004, The geometric thickness of low degree graphs, 340, 10.1145/997817.997868
Geyer, 2009, Two trees which are self-intersecting when drawn simultaneously, Discrete Math., 309, 1909, 10.1016/j.disc.2008.01.033
Malitz, 1994, Graphs with E edges have pagenumber O(E), J. Algorithms, 17, 71, 10.1006/jagm.1994.1027
Barát, 2006, Bounded-degree graphs have arbitrarily large geometric thickness, Electron. J. Combin., 13, R3, 10.37236/1029
Dujmović, 2007, Graph treewidth and geometric thickness parameters, Discrete Comput. Geom., 37, 641, 10.1007/s00454-007-1318-7
R. Blankenship, Book embeddings of graphs, Ph.D. thesis, Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA, 2003.
Blankenship, 2001, Book embeddings of graphs and minor-closed classes
Chandran, 2007, On the Hadwiger's conjecture for graph products, Discrete Math., 307, 266, 10.1016/j.disc.2006.06.019
Lipton, 1979, A separator theorem for planar graphs, SIAM J. Appl. Math., 36, 177, 10.1137/0136016
Alon, 1994, Planar separators, SIAM J. Discrete Math., 7, 184, 10.1137/S0895480191198768
Bodlaender, 1998, A partial k-arboretum of graphs with bounded treewidth, Theoret. Comput. Sci., 209, 1, 10.1016/S0304-3975(97)00228-4
DeVos, 2004, Excluding any graph as a minor allows a low tree-width 2-coloring, J. Combin. Theory Ser. B, 91, 25, 10.1016/j.jctb.2003.09.001
Alon, 1990, A separator theorem for nonplanar graphs, J. Amer. Math. Soc., 3, 801, 10.1090/S0894-0347-1990-1065053-0
Hassin, 1986, Efficient algorithms for optimization and selection on series-parallel graphs, SIAM J. Algebraic Discrete Meth., 7, 379, 10.1137/0607043