A shorter proof of the graph minor algorithm: the unique linkage theorem
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the forty-second ACM symposium on Theory of computing
Linkless and flat embeddings in 3-space and the unknot problem
Proceedings of the twenty-sixth annual symposium on Computational geometry
On graph crossing number and edge planarization
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Isomorphism for graphs of bounded feedback vertex set number
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Strong backdoors to nested satisfiability
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
European Journal of Combinatorics
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
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For every fixed surface $S$, orientable or non-orientable, and a given graph $G$, Mohar (STOC'96 and Siam J. Discrete Math. (1999)) described a linear time algorithm which yields either an embedding of $G$ in $S$ or a minor of $G$ which is not embeddable in $S$ and is minimal with this property. That algorithm, however, needs a lot of lemmas which spanned six additional papers. In this paper, we give a new linear time algorithm for the same problem. The advantages of our algorithm are the following: The proof is considerably simpler: it needs only about 10 pages, and some results (with rather accessible proofs) from graph minors theory, while Mohar's original algorithm and its proof occupy more than 100 pages in total. The hidden constant (depending on the genus $g$ of the surface $S$) is much smaller. It is singly exponential in $g$, while it is doubly exponential in Mohar's algorithm.As a spinoff of our main result, we give another linear time algorithm, which is of independent interest. This algorithm computes the genus and constructs minimum genus embeddings of graphs of bounded tree-width. This resolves a conjecture by Neil Robertson and solves one of the most annoying long standing open question about complexity of algorithms on graphs of bounded tree-width.