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Dominating sets in graphs are often used to model monitoring problems, by posting guards on the vertices of the dominating set. If an (unguarded) vertex is attacked, at least one guard can then react by moving there. This yields a new set of ...

We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding distributed model-...

Local certification consists in assigning labels (called certificates) to the nodes of a network to certify a property of the network or the correctness of a data structure distributed on the network. The verification of this certification must be local:...

Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for all positive integers $a,b$ and a graph $G$, if the treedepth ...

The F-Minor-Free Deletion problem asks, for a fixed set F and an input consisting of a graph G and integer k, whether k vertices can be removed from G such that the resulting graph does not contain any member of F as a minor. At FOCS 2012, Fomin et al. ...

We give asymptotically exact values for the treewidth ${tw}(G)$ of a random geometric graph $G\in{\mathcal G(n,r)}$ in $[0,\sqrt{n}]^2$. More precisely, let $r_c$ denote the threshold radius for the appearance of the giant component in ${\mathcal G(n,r)}$...

In the mixed Chinese postman problem (MCPP), given a weighted mixed graph $G$ (it may have both edges and arcs), our aim is to find a closed walk of minimum weight traversing each edge and arc at least once. The MCPP parameterized by the number of edges ...