6 citations · 8 across the 7 of their papers we have counts for
10 papers
On the Toughness of Regular Graphs and Prisms
Geoffrey Boyer, Wayne Goddard
We contribute results on -regular graphs that do and don't have the maximum possible toughness, namely . Doty and Ferland showed the existence of a -regular graph with t…
Compelling Colorings: A generalization of the dominator chromatic number
Anna Bachstein, Wayne Goddard, Michael A. Henning +1
We define a -compelling coloring as a proper coloring of the vertices of a graph such that every subset consisting of one vertex of each color has property . The -compelli…
Graphs in which all maximal bipartite subgraphs have the same order
Wayne Goddard, Kirsti Kuenzel, Eileen Melville
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite n…
The Generalized Matcher Game
Anna Bachstein, Wayne Goddard, Connor Lehmacher
Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a conta…
The maximum average connectivity among all orientations of a graph
Rocio M. Casablanca, Peter Dankelmann, Wayne Goddard +2
For distinct vertices and in a graph , the {\em connectivity} between and , denoted , is the maximum number of internally disjoint -- paths in …
Colorings with Fractional Defect
Wayne Goddard, Honghai Xu
Consider a coloring of a graph such that each vertex is assigned a fraction of each color, with the total amount of colors at each vertex summing to . We define the fractional d…
Coloring Graphs to Produce Properly Colored Walks
Robert Melville, Wayne Goddard
For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair o…
Thoroughly Distributed Colorings
Wayne Goddard, Michael A. Henning
We consider (not necessarily proper) colorings of the vertices of a graph where every color is thoroughly distributed, that is, appears in every open neighborhood. Equivalently, ev…
Vertex Colorings without Rainbow or Monochromatic Subgraphs
Wayne Goddard, Honghai Xu
This paper investigates vertex colorings of graphs such that some rainbow subgraph~ and some monochromatic subgraph are forbidden. Previous work focussed on the case that $R…
Counting pairs of lattice paths by intersections
Ira Gessel, Wayne Goddard, Walter Shur +2
On an lattice rectangle, we first consider walks that begin at the SW corner, proceed with unit steps in either of the directions E or N, and terminate at the NE co…