general result: The line graph of $G$ is isomorphic to a subgraph of the strong product $H \boxtimes K_{\lfloor p \rfloor}$ for some graph $H$ with treewidth at most $t-2$ and $p = \sqrt{(t-3)\Delta |E(G)|} + \Delta$. [3/3 of https://t.co/ZNR4ZKj20o]
up to the dependency on $t$ and extends earlier results of Diks, Djidjev, Sykora, and Vr\v{t}o (1993) for planar graphs, and of Sykora and Vr\v{t}o (1993) for bounded-genus graphs. Our result is a consequence of the following more [2/3 of https://t.co/Z…
We prove that every $n$-vertex $K_t$-minor-free graph $G$ of maximum degree $\Delta$ has a set $F$ of $O(t^2(\log t)^{1/4}\sqrt{\Delta n})$ edges such that every component of $G - F$ has at most $n/2$ vertices. This is best possible [1/3 of https://t.co…
Gwenaël Joret, William Lochet, Michał T. Seweryn: Edge separators for graphs excluding a minor https://t.co/jjKoMshBbC https://t.co/RHp9lTJn5o