ACM Home Page
Please provide us with feedback. Feedback
An efficient algorithm for the genus problem with explicit construction of forbidden subgraphs
Full text PdfPdf (1.39 MB)
Source Annual ACM Symposium on Theory of Computing archive
Proceedings of the twenty-third annual ACM symposium on Theory of computing table of contents
New Orleans, Louisiana, United States
Pages: 337 - 347  
Year of Publication: 1991
ISBN:0-89791-397-3
Authors
Hristo Djidjev  Bulgarian Academy of Sciences, Sofia, Bulgaria
John Reif  Duke Univ., Durham, NC
Sponsor
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 1,   Downloads (12 Months): 16,   Citation Count: 5
Additional Information:

references   cited by   index terms   collaborative colleagues  

Tools and Actions: Request Permissions Request Permissions    Review this Article  
DOI Bookmark: Use this link to bookmark this Article: http://doi.acm.org/10.1145/103418.103456
What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
Alpert, S.R. The genera of amalgamations of graphs. Trans. Amer. Math. Soc., 178 (1973) 1-39.
 
2
Alpert, S.R., and Gross J.L. Graph Imbedding Problems, in Research Problems (Richard Guy, ed.).
 
3
Battle, J., Harary, F., Kodama, Y., and Youngs, J.W.T. "Additivity of the Genus of a Graph". Bull. Amer. Math. Soc. 68 (1962), 565- 568.
 
4
 
5
Djidjev, H.N., A linear algorithm for partitioning graphs of fixed genus, Serdiea Bulgaricae mathematicae publications, Vol 11, (1985), 369-387.
 
6
Edmonds, J. A combinatorial representation for polyhedral surfaces. Not. Am. Math. Soc. 7 (1960), 646.
 
7
8
 
9
Filotti, I.S. An algorithm for imbedding cubic graphs in the torus, J. Comput. Syst. Sci. 20 (1980), 255-276.
10
11
12
 
13
14
 
15
Khuller, S., S.G. Mitchell, and V.V. Vazirani, "Processor efficient parallel algorithms for the two disjoint paths problem, and for f'mding a Kuratowski homeomorph", 30th Annual Symposium on Foundations of Computer Sceince", Durham, NC, Oct, 1989, p 300- 305
 
16
 
17
Kruskal, J. "Well-quasi-ordering, the tree theorem, and Vazsonyi's conjecture", Trans. Amer. Math. Soc. 95 (1960), 210-225.
 
18
Kuratowski, "Sur le problem des courbes gauches en topologie", Fund. Math. 15 (1930), 271-283.
 
19
Massey, W.S. Algebraic Topology: An Introduction, Harcourt, Brace, and World, New York, 1967.
20
 
21
 
22
ibid, "Isomorphism of k-contractible Graphs (a Generalization of Bounded Valence and Bounded Genus)". Information & Control 65, 1-2 (Jan/Feb 1983), 1-20.
 
23
ibid, An Additivity Theorem for the Genus of a Graph, MIT, TR-85- 342.
 
24
Rarnachandran, V. and J.H. Reif, An optimal parallel algorithm for planarity, 30th Annual Symposium on Foundations of Computer Sceince", Durham, NC, Oct 1989.
 
25
Reif, J. On the Complexity of Extending Partial Imbeddings, Computer Science Dept, Univ Rochester, Technical Report TR33, Oct 1978.
 
26
ibid, Polynomial Time Recognition of Graphs of Fixed Genus, Computer Science Dept, Univ Rochester, Technical Report TR33, Oct 1978.
 
27
Robertson, N., and Seymour, P.D. "Graph minors. I. Excluding a forest", J. Combinatorial Theory (Ser. B), 39-61.
 
28
ibid, "Graph minors. II. Algorithmic aspects of tree-width", J. Algorithms, 7 (1986), 309-322.
 
29
ibid, "Graph minors. HI. Planar tree-width", J. Combinatorial Theory (Ser. B), 49-64.
 
30
 
31
 
32
 
33
ibid, "Graph Minors. XII. Disjoint paths on a surface", preprint, Sept 1986
 
34
 
35
 
36
ibid, "Graph Minors. XVI. Wagner's Conjecture", preprint, to appear
 
37
ibid, "Graph Minors - a Survey", in Survcya in Combinatoricn (I. Anderson, ed.), Cambridge Univ. Press (1985), 153-171.
 
38
 
39
Tutte, W.T. "Combinatorial Oriented Maps". Can. J. Math. 31, 5 (1979), 986-1004.
 
40
Wagner, K. "Uber Einer Eigenshaft der Ebener Complexe", Math. Ann.14 (1937), 570-590.
 
41
White, A.T. Graphs, Groups, and Surfaces, North-Holland, Amsterdam, 1973.
 
42
Youngs, J.W.T. Minimal imbeddings and the genus of a graph, J. Math. Mech., 12 (1963) 303-315. MR 26 #3043.


Collaborative Colleagues:
Hristo Djidjev: colleagues
John Reif: colleagues