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John O’M Bockris,Amulya K. N. Reddyen a knot diagram of treewidth two, does it represent the trivial knot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the trivial knot of treewidth 2 can always be reduced to the trivial

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https://doi.org/10.1007/978-3-642-78677-8ed treewidth is the absence of large cliques. We study graph classes in which this condition is also sufficient, which we call .-bounded. Such graph classes are known to have useful algorithmic applications related to variants of the clique and .-coloring problems. We consider six well-known graph c

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https://doi.org/10.1007/978-981-10-5720-5 In 1981, Lubiw proved that . (.) is .-complete: for each ., we are given a list . of possible images of .. After 35 years, we revive the study of this problem and consider which results for . can be modified to solve ...We prove: 1) Under certain conditions, .-completeness of a class of graphs impl

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