I. Schiermeyer. Deciding 3-colourability in less than O(1.415 n ) steps. Proc. 19th Int. Worksh. Graph-Theoretic Concepts in Computer Science, pp. 177--182. SpringerVerlag, Lecture Notes in Comp. Sci. 790, 1994.  Home/Search Document Not in Database Summary Related Articles Check |
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Small Maximal Independent Sets and Faster Exact Graph Coloring - Eppstein (2001) (3 citations) (Correct)
....(if the graph is 3 chromatic) in time O(3 n 3 ) # 1.4422 n , and an algorithm for finding the chromatic number of an arbitrary graph in time O( 1 3 1 3 ) n ) # 2.4422 n . Since then, the area has grown, and there has been a sequence of papers improving Lawler s 3 coloring algorithm [1,2,4,7], with the most recent algorithm taking time # 1.3289 n . However, there has been no improvement to Lawler s chromatic number algorithm. Lawler s algorithm follows a simple dynamic programming approach, in which we compute the chromatic number not just of G but of all its induced subgraphs. ....
I. Schiermeyer. Deciding 3-colourability in less than O(1.415 n ) steps. Proc. 19th Int. Worksh. Graph-Theoretic Concepts in Computer Science, pp. 177--182. SpringerVerlag, Lecture Notes in Comp. Sci. 790, 1994.
3-Coloring in time O(1.3446^n): a no-MIS algorithm - Beigel, Eppstein (1995) (Correct)
....the following very simple algorithm for 3 coloring: for each maximal independent set, test whether the complement is bipartite. The maximal independent sets can be listed with polynomial delay [4] and there are at most 3 n=3 such sets [6] so this algorithm takes time O(1:4422 n ) Schiermeyer [10] gives a complicated algorithm for solving 3 colorability in time O(1:415 n ) based on the following idea: if there is one vertex v of degree n Gamma 1 then the graph is 3 colorable iff G Gamma v is bipartite, and the problem is easily solved. Otherwise, Schiermeyer performs certain ....
I. Schiermeyer. Deciding 3-colourability in less than O(1:415 n ) steps. 19th Int. Worksh. Graph-Theoretic Concepts in Computer Science, Springer-Verlag (1994) 177--182.
3-Coloring in time O(1.3446^n): a no-MIS algorithm - Beigel, Eppstein (1995) (Correct)
....following very simple algorithm for 3 coloring: for each maximal independent set, test whether the complement is bipartite. The maximal independent sets can be listed with polynomial delay [5] and there are at most 3 n=3 such sets [10] so this algorithm takes time O(1:4422 n ) Schiermeyer [15] gives a complicated algorithm for solving 3 colorability in time O(1:415 n ) based on the following idea: if there is one vertex v of degree n Gamma 1 then the graph is 3 colorable iff G Gamma v is bipartite, and the problem is easily solved. Otherwise, Schiermeyer performs certain ....
I. Schiermeyer. Deciding 3-colourability in less than O(1:415 n ) steps. 19th Int. Worksh. Graph-Theor. Concepts C. S., Springer-Verlag (1994) 177--182.
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