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13 papers · 2 filters
Median eigenvalues of bipartite graphs
Bojan Mohar, Behruz Tayfeh-Rezaie
For a graph of order and with eigenvalues , the HL-index is defined as $R(G) ={\max}\left\{|λ_{\lfloor(n+1)/2\rfloor}|, |λ_{\lceil(n+…
Forbidden minors for graphs with no first obstruction to parametric Feynman integration
Samson Black, Iain Crump, Matt DeVos +1
We give a characterization of 3-connected graphs which are planar and forbid cube, octahedron, and minors, where is the graph which is one away from each of the cube…
Median eigenvalues of bipartite subcubic graphs
Bojan Mohar
It is proved that the median eigenvalues of every connected bipartite graph of maximum degree at most three belong to the interval with a single exception of the Heawo…
The robber strikes back
Anthony Bonato, Stephen Finbow, Przemyslaw Gordinowicz +5
We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, t…
Beyond Ohba's Conjecture: A bound on the choice number of -chromatic graphs with vertices
Jonathan A. Noel, Douglas B. West, Hehui Wu +1
Let denote the choice number of a graph (also called "list chromatic number" or "choosability" of ). Noel, Reed, and Wu proved the conjecture of Ohba that $\t…
Point determining digraphs, -matrix partitions, and dualities in full homomorphisms
Pavol Hell, César Hernández-Cruz
We prove that every point-determining digraph contains a vertex such that is also point determining. We apply this result to show that for any -matrix , w…
Wieferich pairs and Barker sequences, II
Peter Borwein, Michael J. Mossinghoff
We show that if a Barker sequence of length exists, then either , or . This improves the lower bound on the length o…
On edge-sets of bicliques in graphs
Marina Groshaus, Pavol Hell, Juraj Stacho
A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the a…
Packing Steiner Trees
Matt DeVos, Jessica McDonald, Irene Pivotto
Let be a distinguished subset of vertices in a graph . A -\emph{Steiner tree} is a subgraph of that is a tree and that spans . Kriesell conjectured that contai…
Polynomial-time perfect matchings in dense hypergraphs
Peter Keevash, Fiachra Knox, Richard Mycroft
Let be a -graph on vertices, with minimum codegree at least for some fixed . In this paper we construct a polynomial-time algorithm which finds either…
Towards a Combinatorial Understanding of Lattice Path Asymptotics
Samuel Johnson, Marni Mishna, Karen Yeats
We provide a new strategy to compute the exponential growth constant of enumeration sequences counting walks in lattice path models restricted to the quarter plane. The bounds aris…
On Double 3-Term Arithmetic Progressions
Tom Brown, Veselin Jungić, Andrew Poelstra
In this note we are interested in the problem of whether or not every increasing sequence of positive integers with bounded gaps must contain a double 3-term arithme…
Singularity analysis via the iterated kernel method
Stephen Melczer, Marni Mishna
In the quarter plane, five lattice path models with unit steps have resisted the otherwise general approach of Fayolle, Rachel, and Kurkova. Here we consider these five models, cal…