Titlebook: ;

Malleable

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,Hamiltonicity Below Dirac’s Condition,ptotically optimal, under the exponential-time hypothesis (ETH)..The results extend the range of tractability of the . problem, showing that it is fixed-parameter tractable when parameterized below a natural bound. In addition, for the first parameterization we show that a kernel with .(.) vertices can be found in polynomial time.

預(yù)防注射

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,Fixed-Parameter Tractability of Counting Small Minimum (,,?,)-Cuts,’s theorem, allows us to build the algorithm counting all minimum (.,?.)-cuts with running time .. Initially dedicated to counting minimum cuts, it can be modified to obtain an FPT sampling of minimum edge (.,?.)-cuts.

燒烤

Travelling on Graphs with Small Highway Dimension,a fully-polynomial time approximation scheme (FPTAS). We also prove that STP is weakly .-hard for these restricted graphs. For TSP we show .-hardness for graphs of highway dimension?6, which answers an open problem posed in [Feldmann?et al.?ICALP?2015].

FRET

Approximating Minimum Dominating Set on String Graphs, we also provide an 8-approximation for the . problem for the . L-., intersection graphs of .-paths intersecting a common vertical line. The same problem is known to be APX-Hard (MFCS, 2018). As a by-product of our proof, we obtained a 2-approximation algorithm for the . (.) problem introduced and studied by Katz et al. (Comput. Geom. 2005).

打折

Philip M. Dean,Richard A. Lewisubgraph-free graph, using as parameter the vertex-deletion distance to treewidth ., where . denotes the minimum treewidth of the graphs in .. For the other case, where . contains a .-subgraph-free graph, we present a polynomial Turing kernelization. Our results extend to .-.-..

猛擊

https://doi.org/10.1007/978-1-349-11044-5 the flip distance between graph orientations in which every cycle has a specified number of forward edges, and a flip is the reversal of all edges in a minimal directed cut. In general, the problem remains hard, but if we only change sinks into sources, or vice-versa, then the problem can be solved in polynomial time.

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