We study the following simultaneous embedding problem: Given k graphs on the same vertex set with the same pairwise intersection, do they admit planar drawings that coincide on their shared graph? We establish fixed-parameter tractability with respect to the vertex integrity of the union graph (that is, the union of th...
Thomas Depian, S. D. Fink, Alexander Firbas et al.· 0 citations
It is shown that Pattern Avoidance is $\Sigma_2^{\textsf{P}}$-complete and furthermore remains intractable (in both the classical and parameterized sense) even under a variety of severe restrictions to both the pattern $P$ and the graph $G$.
Thomas Depian, S. D. Fink, Alexander Firbas et al.· 0 citations
This paper investigates the parameterized complexity of this problem and obtains an ETH-tight single-exponential algorithm for the classical unconstrained version of the problem, improving upon the previous $O^*(2^{k\cdot k})$ algorithms.
Alexander Firbas, R. Ganian, Sylvain Meunier et al.· arXiv.org· 0 citations
This paper proves that the former two problems are fixed-parameter tractable when parameterized by the treedepth of the input graph, and shows that Set of Degrees MST remains W[1]-hard parameterized by treedepth, even when combined with the feedback vertex number.
Narek Bojikian, Alexander Firbas, Robert Ganian et al.· 0 citations
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