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17 papers · 2 filters
Thoughts on Barnette's Conjecture
Helmut Alt, Michael S. Payne, Jens M. Schmidt +1
We prove a new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian. This condition is most easily described as a property of the dual graph. Let be a pl…
What is Ramsey-equivalent to a clique?
Jacob Fox, Andrey Grinshpun, Anita Liebenau +2
A graph G is Ramsey for H if every two-colouring of the edges of G contains a monochromatic copy of H. Two graphs H and H' are Ramsey-equivalent if every graph G is Ramsey for H if…
On the multicolor Ramsey number of a graph with m edges
Kathleen Johst, Yury Person
The multicolor Ramsey number of a graph is the least integer such that in every coloring of the edges of by colors there is a monochromatic copy of .…
On counterexamples to a conjecture of Wills and Ehrhart polynomials whose roots have equal real parts
Matthias Henze
As a discrete analog to Minkowski's theorem on convex bodies, Wills conjectured that the Ehrhart coefficients of a centrally symmetric lattice polytope with exactly one interior la…
On the limiting distribution of the metric dimension for random forests
Dieter Mitsche, Juanjo Rué
The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. I…
A linear bound on the Manickam-Miklos-Singhi Conjecture
Alexey Pokrovskiy
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of k numbers from {x_1, ..., x_n} must have nonnegative sum? Manickam, Miklos, and…