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cs.DM2017
Simple cubic graphs with no short traveling salesman tour
Robert Lukoťka, Ján Mazák
Let denote the length of a shortest travelling salesman tour in a graph . We prove that for any , there exists a simple -connected planar cubic graph…
cs.DM2016
Weak oddness as an approximation of oddness and resistance in cubic graphs
Robert Lukoťka, Ján Mazák
We introduce weak oddness , a new measure of uncolourability of cubic graphs, defined as the least number of odd components in an even factor. For every bridgeless c…
cs.DM2012★ 2 cited
Small snarks with large oddness
Robert Lukotka, Edita Macajova, Jan Mazak +1
We estimate the minimum number of vertices of a cubic graph with given oddness and cyclic connectivity. We prove that a bridgeless cubic graph with oddness other than th…