Lancaster City Council

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20132026

most citedSingle-photon detection in the mid-infrared up to 10 micron wavelength using tungsten silicide superconducting nanowire detectors

141 citations

Showing math.COShow all

3 papers · 1 filter

math.CO2016

Edge Lower Bounds for List Critical Graphs, via Discharging

Daniel W. Cranston, Landon Rabern

A graph $G$ is $k$ -critical if $G$ is not $(k - 1)$ -colorable, but every proper subgraph of $G$ is $(k - 1)$ -colorable. A graph $G$ is $k$ -choosable if $G$ has an $L$ -coloring from eve…

math.CO2014

A note on coloring vertex-transitive graphs

Daniel W. Cranston, Landon Rabern

We prove bounds on the chromatic number $χ$ of a vertex-transitive graph in terms of its clique number $ω$ and maximum degree $Δ$ . We conjecture that every vertex-transitive graph…

math.CO2013

Graphs with $χ = Δ$ have big cliques

Daniel W. Cranston, Landon Rabern

Brooks' Theorem states that if a graph has $Δ \geq 3$ and $ω \leq Δ$ , then $χ \leq Δ$ . Borodin and Kostochka conjectured that if $Δ \geq 9$ and $ω \leq Δ - 1$ , then $χ \leq Δ - 1$ . We show that if…

Edge Lower Bounds for List Critical Graphs, via Discharging

A note on coloring vertex-transitive graphs

Graphs with χ=Δ have big cliques

Graphs with $χ = Δ$ have big cliques