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9 papers · 2 filters
On Weak Flexibility in Planar Graphs
Bernard Lidický, Tomáš Masařík, Kyle Murphy +1
Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs [JGT 19']. In this new setting, each vertex in some subset of has a…
On a conjecture by Anthony Hill
Bojan Mohar
In the 1950's, English painter Anthony Hill described drawings of complete graphs in the plane having precisely $$H(n) = \tfrac{1}{4}\lfloor \tfrac{n}{2}\rfloor \, \lfloor \t…
Flexible List Colorings in Graphs with Special Degeneracy Conditions
Peter Bradshaw, Tomáš Masařík, Ladislav Stacho
For a given , we say that a graph is -flexibly -choosable if the following holds: for any assignment of color lists of size on ,…
On Conjectures Concerning the Smallest Part and Missing Parts of Integer Partitions
Damanvir Singh Binner, Amarpreet Rattan
For positive integers and , Berkovich and Uncu (Ann. Comb. () --) conjectured an inequality between the sizes of two closely related sets of part…
Many flows in the group connectivity setting
Matt DeVos, Rikke Langhede, Bojan Mohar +1
Two well-known results in the world of nowhere-zero flows are Jaeger's 4-flow theorem asserting that every 4-edge-connected graph has a nowhere-zero $\mathbb{Z}_2 \times \mathbb{Z}…
List homomorphism problems for signed trees
Jan Bok, Richard Brewster, Tomás Feder +2
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph $…
Constructions of difference sets in nonabelian 2-groups
Taylor Applebaum, John Clikeman, James A. Davis +5
Difference sets have been studied for more than 80 years. Techniques from algebraic number theory, group theory, finite geometry, and digital communications engineering have been u…
A new representation of mutually orthogonal frequency squares
Jonathan Jedwab, Tabriz Popatia
Mutually orthogonal frequency squares (MOFS) of type generalize the structure of mutually orthogonal Latin squares: rather than each of symbols appearing exactly once…
Simple eigenvalues of cubic vertex-transitive graphs
Krystal Guo, Bojan Mohar
If is an eigenvector for eigenvalue of a graph and is an automorphism of , then is also an eigenvector for . Thus it is rather exceptional for an eigen…