Bojan Mohar
- 1.D. Archdeacon, The complexity of the graph embedding problem, in "Topics in Combinatorics and Graph Theory," R. Bodendiek and R. Henn (Eds.), Physica- Verlag, Heidelberg, 1990, pp. 59-64.Google Scholar
- 2.D. Archdeacon, P. Huneke, A Kuratowski theorem for nonorientable surfaces, J. Combin. Theory Ser. B 46 (1989) 173-231. Google ScholarDigital Library
- 3.J. Battle, F. Harary, Y. Kodama, J. W. T. Youngs, Additivity of the genus of a graph, Bull. Amer. Math. Soc. 68 (1962) 565-568.Google ScholarCross Ref
- 4.K. S. Booth, G. S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-trees, J. Comput. System Sci. 13 (1976) 335- 379.Google ScholarDigital Library
- 5.N. Chiba, T. Nishizeki, S. Abe, T. Ozawa, A linear algorithm for embedding planax graphs using PQ-trees, J. Comput. System Sci. 30 (1985) 54-76. Google ScholarDigital Library
- 6.S. A. Cook, R. A. Reckhow, Time bounded random access machines, J. Comput. Syst. Sci. 7 (1976) 354- 375.Google ScholarDigital Library
- 7.H. Djidjev, J. H. Reif, An efficient algorithm for the genus problem with explicit construction of forbidden subgraphs, 23rd Annual ACM Symposium on Theory of Computing, New Orleans, LA, May 1991, pp. 337-347. Google ScholarDigital Library
- 8.I. S. Filotti, G. L. Miller, J. Reif, On determining the genus of a graph in O(v~(g)) steps, in "Proc. 11th Ann. ACM STOC," Atlanta, Georgia (1979) pp. 27-37. Google ScholarDigital Library
- 9.J. L. Gross, T. W. Tucker, Topological graph theory, Wiley-Interscience, New York, 1987. Google ScholarDigital Library
- 10.J. E. Hopcroft, P~. E. Tarjan, Dividing a graph into triconnected components, SIAM J. Comput. 2 (1973) 135-158.Google ScholarCross Ref
- 11.J. E. Hopcroft, R. E. Taxjan, Efficient planarity testing, J. ACM 21 (1974) 549-568. Google ScholarDigital Library
- 12.M. Juvan, J. MaxinSoek, B. Mohar, Elimination of local bridges, Math. Slovaca, to appear.Google Scholar
- 13.M. Juvan, J. Marin~ek, B. Mohar, Obstructions for simple embeddings, preprint, 1994.Google Scholar
- 14.M. Juvan, J. Maxin~:ek, B. Mohax, Embedding a graph into the torus in linear time, preprint, 1994.Google Scholar
- 15.M. Juvan, B. Mohar, Extending 2-restricted partial embeddings of graphs, preprint, 1995.Google Scholar
- 16.A. Karabeg, Classification and detection of obstructions to planarity, Lin. Multilin. Algebra 26 (1990) 15- 38.Google ScholarCross Ref
- 17.B. Mohar, Projective planarity in linear time, J. Algorithms 15 (1993) 482-502. Google ScholarDigital Library
- 18.B. Mohar, Obstructions for the disk and the cylinder embedding extension problems, Combin. Probab. Cornput. 3 (1994) 375-406.Google ScholarCross Ref
- 19.B. Mohar, Universal obstructions for embedding extension problems, preprint, 1994.Google Scholar
- 20.B. Mohar, C. Thomassen, Graphs on surfaces.Google Scholar
- 21.N. Robertson, P. D. Seymour, Graph minors. VIII. A Kuratowski theorem for general surfaces, J. Combin. Theory, Ser. B 48 (1990) 255-288. Google ScholarDigital Library
- 22.N. Robertson, P. D. Seymour, Graph minors. XIII. The disjoint paths problem, J. Combin. Theory, Ser. B 63 (1995) 65-110. Google ScholarDigital Library
- 23.N. Robertson, P. D. Seymour, Graph minors. XXI. Graphs with unique linkages, preprint, 1992.Google Scholar
- 24.N. Robertson, P. D. Seymour, Graph minors. XXII. Irrelevant vertices in linkage problems, preprint, 1992.Google Scholar
- 25.N. Robertson, P. D. Seymour, An outline of a disjoint paths algorithm, in: "Paths, Flows, and VLSI-Layout" (B. Korte, L. Lov~sz, H. J. Pr5mel and A. Schrijver eds.), Springer-Verlag, Berlin, 1990, pp. 267--292.Google Scholar
- 26.P. D. Seymour, A bound on the excluded minors for a surface, submitted.Google Scholar
- 27.S. Stahl, L. W. Beineke, Blocks and the nonorientable genus of graphs, j. Graph Theory i (1977) 75-78.Google Scholar
- 28.C. Thomassen, The graph genus problem is NP- complete, J. Algorithms 10 (1989) 568-576. Google ScholarDigital Library
- 29.C. Thomassen, Triangulating a surface with a prescribed graph, J. Combin. Theory Ser. B 57 (1993) 196- 206. Google ScholarDigital Library
- 30.S. G. Williamson, Embedding graphs in the plane algorithmic aspects, Ann. Discrete Math. 6 (1980) 349- 384.Google ScholarCross Ref
- 31.S. G. Williamson, Depth-first search and Kuratowski subgraphs, J. ACM 31 (1984) 681-693. Google ScholarDigital Library
Index Terms
- Embedding graphs in an arbitrary surface in linear time
Recommendations
A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface
For an arbitrary fixed surface S, a linear time algorithm is presented that for a given graph G either finds an embedding of G in S or identifies a subgraph of G that is homeomorphic to a minimal forbidden subgraph for embeddability in S. A side result ...
Linear choosability of graphs
A proper vertex coloring of a non-oriented graph G is linear if the graph induced by the vertices of any two color classes is a forest of paths. A graph G is linearly L-list colorable if for a given list assignment L={L(v):v@?V(G)}, there exists a ...
Comments