Hudson Lafayette

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t

-Tone Chromatic Number of Classes of Sparse Graphs

1 citations · 1 across the 1 of their papers we have counts for

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2 papers

math.CO2022★ 1 cited

The $t$ -Tone Chromatic Number of Classes of Sparse Graphs

Daniel W. Cranston, Hudson LaFayette

For a graph $G$ and $t, k \in Z^{+}$ a \emph{ $t$ -tone $k$ -coloring} of $G$ is a function $f : V (G) \to (t [ k ])$ such that $∣ f (v) \cap f (w) ∣ < d (v, w)$ for all distinc…

math.CO2020

Coloring $(P_{5}, gem)$ -free graphs with $Δ - 1$ colors

Daniel W. Cranston, Hudson Lafayette, Landon Rabern

The Borodin-Kostochka Conjecture states that for a graph $G$ , if $Δ (G) \geq 9$ and $ω (G) \leq Δ (G) - 1$ , then $χ (G) \leq Δ (G) - 1$ . We prove the Borodin-Kostochka Conjecture for $(P_5,…

The t-Tone Chromatic Number of Classes of Sparse Graphs

Coloring (P5​,gem)-free graphs with Δ−1 colors

The $t$ -Tone Chromatic Number of Classes of Sparse Graphs

Coloring $(P_{5}, gem)$ -free graphs with $Δ - 1$ colors