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Speaker: Haiko Muller, School of Computing, University of Leeds Title: On a disparity between relative cliquewidth and relative NLC-width Abstract: Cliquewidth and NLC-width are two closely related parameters that measure the complexity of graphs. Both clique- and NLC-width are defined to be the minimum number of labels required to create a labelled graph by certain terms of operations. Many hard problems on graphs become solvable in polynomial time if the inputs are restricted to graphs of bounded clique- or NLC-width. Cliquewidth and NLC-width differ at most by a factor of two. The relative counterparts of these parameters are defined to be the minimum number of labels necessary to create a graph while the tree-structure of the term is fixed. We show that RELATIVE CLIQUEWIDTH and RELATIVE NLC-WIDTH differ significantly in computational complexity. While the former problem is NP-complete the latter is solvable in polynomial time. The relative NLC-width can be computed in O(n^3) time, which also yields an exact algorithm for computing the NLC-width in time O(3^{n}n). Additionally, our technique enables a combinatorial characterisation of NLC-width that avoids the usual operations on labelled graphs.