Abstract
We present a linear time algorithm which determines whether an input graph contains K 5 as a minor and outputs a K 5-model if the input graph contains one. If the input graph has no K 5-minor then the algorithm constructs a tree decomposition such that each node of the tree corresponds to a planar graph or a graph with eight vertices. Such a decomposition can be used to obtain algorithms to solve various optimization problems in linear time. For example, we present a linear time algorithm for finding an \(O(\sqrt{n})\) seperator and a linear time algorithm for solving k-realisation on graphs without a K 5-minor. Our algorithm will also be used, in a separate paper, as a key subroutine in a nearly linear time algorithm to test for the existence of an H-minor for any fixed H.
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Reed, B., Li, Z. (2008). Optimization and Recognition for K 5-minor Free Graphs in Linear Time. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_18
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DOI: https://doi.org/10.1007/978-3-540-78773-0_18
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