Brewster, Richard C.


Cycles in Graphs of Large Chromatic Number ★★

Author(s): Brewster; McGuinness; Moore; Noel

\begin{conjecture} If $\chi(G)>k$, then $G$ contains at least $\frac{(k+1)(k-1)!}{2}$ cycles of length $0\bmod k$. \end{conjecture}

Keywords: chromatic number; cycles

Mixing Circular Colourings

Author(s): Brewster; Noel

\begin{question} Is $\mathfrak{M}_c(G)$ always rational? \end{question}

Keywords: discrete homotopy; graph colourings; mixing

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