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8 papers · 2 filters
Long Cycles and Spanning Subgraphs of Locally Maximal 1-planar Graphs
Igor Fabrici, Jochen Harant, Tomáš Madaras +3
A graph is -planar if it has a drawing in the plane such that each edge is crossed at most once by another edge. Moreover, if this drawing has the additional property that for e…
Large independent sets in triangle-free cubic graphs: beyond planarity
Wouter Cames van Batenburg, Jan Goedgebeur, Gwenaël Joret
Every -vertex planar triangle-free graph with maximum degree at most has an independent set of size at least . This was first conjectured by Albertson, Bollobá…
Eigenvalues, Smith normal form and determinantal ideals
Aida Abiad, Carlos A. Alfaro, Kristin Heysse +1
Determinantal ideals of graphs generalize, among others, the spectrum and the Smith normal form (SNF) of integer matrices associated to graphs. In this work we investigate the rela…
Generation of Local Symmetry-Preserving Operations
Pieter Goetschalckx, Kris Coolsaet, Nico Van Cleemput
We introduce a new practical and more general definition of local symmetry-preserving operations on polyhedra. These can be applied to arbitrary plane graphs and result in plane gr…
Small weight code words arising from the incidence of points and hyperplanes in PG()
Sam Adriaensen, Lins Denaux, Leo Storme +1
Let be the code arising from the incidence of points and hyperplanes in the Desarguesian projective space PG(). Recently, Polverino and Zullo proved that within…
Maps related to polar spaces preserving a Weyl distance or an incidence condition
A. De Schepper, H. Van Maldeghem
Let and be the sets of elements of respective types and of a polar space~ of rank at least , viewed as a Tits-building. For any Weyl distance between…