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 2010Show all

6 papers · 1 filter

math.CO2010★ 1 cited

Linear Choosability of Sparse Graphs

Daniel W. Cranston, Gexin Yu

We study the linear list chromatic number, denoted $\lcl(G)$, of sparse graphs. The maximum average degree of a graph $G$ , denoted $\mad(G)$, is the maximum of the average degrees…

math.CO2010

Overlap Number of Graphs

Daniel W. Cranston, Nitish Korula, Timothy D. LeSaulnier +4

An {\it overlap representation} of a graph $G$ assigns sets to vertices so that vertices are adjacent if and only if their assigned sets intersect with neither containing the other…

math.CO2010

Injective colorings of sparse graphs

Daniel W. Cranston, Seog-Jin Kim, Gexin Yu

Let $ma d (G)$ denote the maximum average degree (over all subgraphs) of $G$ and let $χ_{i} (G)$ denote the injective chromatic number of $G$ . We prove that if $ma d (G) \leq 5/2$ , then $…

math.CO2010

Crossings, colorings, and cliques

Michael O. Albertson, Daniel W. Cranston, Jacob Fox

Albertson conjectured that if graph $G$ has chromatic number $r$ , then the crossing number of $G$ is at least that of the complete graph $K_{r}$ . This conjecture in the case $r = 5$ is…

math.CO2010

A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid

Daniel W. Cranston, Gexin Yu

Given a graph $G$ , an identifying code $C \subseteq V (G)$ is a vertex set such that for any two distinct vertices $v_{1}, v_{2} \in V (G)$ , the sets $N [v_{1}] \cap C$ and $N [v_{2}] \cap C$ are…

math.CO2010

Injective colorings of graphs with low average degree

Daniel W. Cranston, Seog-Jin Kim, Gexin Yu

Let $\mad(G)$ denote the maximum average degree (over all subgraphs) of $G$ and let $χ_{i} (G)$ denote the injective chromatic number of $G$ . We prove that if $Δ \geq 4$ and $\mad(G)<\…