Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Gro¨tzsch's 3-color theorem and its counterparts for the torus and the projective plane
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Theoretical Computer Science
Depth-First Search and Kuratowski Subgraphs
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The chromatic number of a graph of girth 5 on a fixed surface
Journal of Combinatorial Theory Series B
A short list color proof of Grötzsch's theorem
Journal of Combinatorial Theory Series B
Three-coloring Klein bottle graphs of girth five
Journal of Combinatorial Theory Series B
Oracles for bounded-length shortest paths in planar graphs
ACM Transactions on Algorithms (TALG)
Coloring triangle-free graphs on surfaces
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 3 - Volume 3
Sub-exponentially many 3-colorings of triangle-free planar graphs
Journal of Combinatorial Theory Series B
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Grötzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring in linear time (Kowalik used a nontrivial data structure to construct an O(n log n) algorithm). We design a linear-time algorithm to find a 3-coloring of a given triangle-free planar graph. The algorithm avoids using any complex data structures, which makes it easy to implement. As a by-product we give a yet simpler proof of Grötzsch's theorem.