k-cacti exclude large complete minors and thus have edge density O((log k / sqrt(log log k)) n), tight up to a sqrt(log log k) factor.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Improves exact algorithm for minimum edge deletion to connected cactus from O*(3^n) to O*(2^n), with O*(2^n n^{O(q)}) for q distinct nonnegative costs and O*(2^n (W+1)) pseudo-polynomial for integer costs summing to W.
citing papers explorer
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The density of $k$-cacti via excluding minors
k-cacti exclude large complete minors and thus have edge density O((log k / sqrt(log log k)) n), tight up to a sqrt(log log k) factor.
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Exact Algorithms for Edge Deletion to Cactus Graphs and Weighted Variants
Improves exact algorithm for minimum edge deletion to connected cactus from O*(3^n) to O*(2^n), with O*(2^n n^{O(q)}) for q distinct nonnegative costs and O*(2^n (W+1)) pseudo-polynomial for integer costs summing to W.