9 papers
Two Distinct Eigenvalues from a New Graph Product
Eric Culver, Mark Kempton
The parameter of a graph is the minimum number of distinct eigenvalues of a symmetric matrix whose pattern is given by . We introduce a novel graph product by which w…
On odd covers of cliques and disjoint unions
Calum Buchanan, Alexander Clifton, Eric Culver +5
Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order…
Domination of subcubic planar graphs with large girth
Eun-Kyung Cho, Eric Culver, Stephen G. Hartke +1
Since Reed conjectured in 1996 that the domination number of a connected cubic graph of order is at most , the domination number of cubic graphs has be…
Path Odd-Covers of Graphs
Steffen Borgwardt, Calum Buchanan, Eric Culver +3
We introduce and study "path odd-covers", a weakening of Gallai's path decomposition problem and a strengthening of the linear arboricity problem. The "path odd-cover number" $p_2(…
Square of Planar Graphs of Max Degree Four without Five Cycles
Eric Culver, Stephen G. Hartke
We show that the choosability of the square of planar graphs of max degree 4 without five cycles is at most 12. Keywords: planar graph, choosability AMS Mathematics Subject Classif…
On Sums, Derivatives, and Flips of Riordan Arrays
Caroline Bang, Matias von Bell, Eric Culver +4
We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the - and -sequences of these…
Relation between the correspondence chromatic number and the Alon--Tarsi number
Eric Culver, Stephen Hartke
We study the relation between the correspondence chromatic number and the Alon--Tarsi number, both upper bounds on the list chromatic number of a graph. There are many graphs with…
Odd Covers of Graphs
Calum Buchanan, Alexander Clifton, Eric Culver +4
Given a finite simple graph , an odd cover of is a collection of complete bipartite graphs, or bicliques, in which each edge of appears in an odd number of bicliques and…
Entropy of Tournament Digraphs
David E. Brown, Eric Culver, Bryce Frederickson +2
The Rényi -entropy of complete antisymmetric directed graphs (i.e., tournaments) is explored. We optimize when and , and find that as increases 's…