D. Cranston

activity

20052026

most citedA Note on Odd Colorings of 1-Planar Graphs

22 citations · 92 across the 73 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.CO2017

A Characterization of $(4, 2)$ -Choosable Graphs

Daniel W. Cranston

A graph $G$ is \emph{ $(a, b)$ -choosable} if given any list assignment $L$ with $∣ L (v) ∣ = a$ for each $v \in V (G)$ there exists a function $φ$ such that $φ (v) \in L (v)$ and $∣ φ (v) ∣ = b$ fo…

math.CO2017

Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5

Daniel W. Cranston

The distinguishing chromatic number, $χ_{D} (G)$ , of a graph $G$ is the smallest number of colors in a proper coloring, $φ$ , of $G$ , such that the only automorphism of $G$ that preser…

math.CO2017

Acyclic edge-coloring of planar graphs: $Δ$ colors suffice when $Δ$ is large

Daniel W. Cranston

An \emph{acyclic edge-coloring} of a graph $G$ is a proper edge-coloring of $G$ such that the subgraph induced by any two color classes is acyclic. The \emph{acyclic chromatic inde…

math.CO2017

The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4

Daniel W. Cranston, Landon Rabern

A simple graph $G$ is \emph{overfull} if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . By the pigeonhole principle, every overfull graph $G$ has $χ^{'} (G) > Δ$ . The \emph{core} of a graph, denoted…

A Characterization of (4,2)-Choosable Graphs

Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5

Acyclic edge-coloring of planar graphs: Δ colors suffice when Δ is large

The Hilton--Zhao Conjecture is True for Graphs with Maximum Degree 4

A Characterization of $(4, 2)$ -Choosable Graphs

Acyclic edge-coloring of planar graphs: $Δ$ colors suffice when $Δ$ is large