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Complexity properties of complementary prisms
TLDR
This work studies algorithmic/complexity properties of complementary prisms with respect to cliques, independent sets, k-domination, and especially $$P_3$$P3-convexity.
On the (Parameterized) Complexity of Recognizing Well-Covered (r, l)-graphs
TLDR
It is shown that the parameterized problem of deciding whether a general graph is well-covered parameterized by \(\alpha \) can be reduced to the wc \((0,\ell )\) g problem parameterizing by \(\ell \), and it is proved that this latter problem is in XP but does not admit polynomial kernels unless \(\mathsf{coNP} \subseteq \ mathsf{NP} / \mathSF{poly}\).
Hitting forbidden induced subgraphs on bounded treewidth graphs
TLDR
The smallest function $f_H(t)$ such that H-IS-Deletion can be solved in time is determined assuming the Exponential Time Hypothesis (ETH), and it is shown that when $H$ deviates slightly from a clique, the function suffers a sharp jump.
Computing the largest bond of a graph
TLDR
It is shown that {\sc Largest Bond} remains NP-hard even for planar bipartite graphs, and it does not admit a constant-factor approximation algorithm, unless $P = NP, and both problems are fixed-parameter tractable when parameterized by the size of the solution, but they do not admit polynomial kernels unless NP $\subseteq coNP/poly.
On Colored Edge Cuts in Graphs
TLDR
This work is interested in problems of finding cuts {A,B} which minimize or maximize the number of colors occurring in the edges with exactly one endpoint in A.
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