TY - CONF
AB - Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.
AU - Huszár, Kristóf
AU - Spreer, Jonathan
ID - 6556
KW - computational 3-manifold topology
KW - fixed-parameter tractability
KW - layered triangulations
KW - structural graph theory
KW - treewidth
KW - cutwidth
KW - Heegaard genus
SN - 1868-8969
T2 - 35th International Symposium on Computational Geometry (SoCG 2019)
TI - 3-manifold triangulations with small treewidth
VL - 129
ER -