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${\sf sbn}(G) \leq k$ is an ${\sf NP}$-complete problem. [8/8 of https://t.co/Os5Rs3J6L0]
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$k$-domino-tree. We also identify three graphs that constitute the minor-obstruction set of the class of graphs with strict bramble number at most two. We complete our results by proving that, given some $G$ and $k,$ deciding whether [7/8 of https://t.c…
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width at most $k.$ The third characterization is in terms of extremal graphs. For this, we define, for each $k,$ the concept of a $k$-domino-tree and we prove that every edge-maximal graph of strict bramble number at most $k$ is a [6/8 of https://t.co/O…
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second characterization is in terms of a new variant of a tree decomposition called lenient tree decomposition. We prove that ${\sf sbn}(G)$ is equal to the minimum $k$ for which there exists a lenient tree decomposition of $G$ of [5/8 of https://t.co/O…