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Claim. S. Wagon, A bound on the chromatic number of graphs without certain induced subgraphs, J. Combin. Theory Ser. B 29 (1980), no. 3, 345--346, proves the Theorem (p. 345): "If the graph $G$ does not contain the complement of a chordless 4-cycle as an induced subgraph, then $\chi(G)\le\binom{\omega(G)+1}2$." The excluded graph is $K_2\cup K_2$. Two anticomplete sets of chromatic number at least $2$ each contain an edge, and the two edges induce $K_2\cup K_2$; so a graph with $\omega(G)<t$ and no such sets has $\chi(G)\le\binom{\omega(G)+1}2\le\binom t2$. Hence $d(t,2)\le\binom t2+1$ for Problem 1111, as El-Zahar and Erdős note (Combinatorica 5 (1985), p. 296) and the site's commentary credits.

Covers. The case $c=2$ of the statement, for every $t$.

Depends on. No page of this wiki: the one-line deduction of $d(t,2)\le\binom t2+1$ from the Theorem is written above, as on the problem page.

Acceptance. Refereed: J. Combin. Theory Ser. B 29 (1980), no. 3, 345--346 (Crossref: December 1980; the day is the issue's nominal first day, used for this page's date). The site labels the problem OPEN, so its commentary crediting the result is not review, and no reviewed evidence is listed.