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Claim. N. Wormald, A 4-chromatic graph with a special plane drawing, J. Austral. Math. Soc. Ser. A 28 (1979), no. 1, 1–8 (source card), exhibits a finite set of $6448$ points in the plane whose unit distance graph, with an edge exactly when two points are at distance $1$, has girth $5$ and chromatic number $4$. The abstract graph attaches a $5$-cycle to each $5$-subset of $13$ ordered points; a $3$-coloring would make some $5$-subset monochromatic and leave its attached $5$-cycle two colors, which is impossible. The plane realization is shown to exist by continuity arguments checked by computer. In the terms of Problem 705, no $k\le5$ makes every finite unit distance graph of girth at least $k$ $3$-colorable.

Covers. No $k\le5$ works. Nothing is settled for $k\ge6$; that case is settled by O'Donnell's dissertation.

Depends on. No page of this wiki.

Standing. Accepted on its refereed publication in the Journal of the Australian Mathematical Society. The curator's label credits O'Donnell's dissertation, not this paper, so reviewed is not listed.

Dating. Crossref dates the issue August 1979; the day is a placeholder.