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The claim. S. Cambie and M. Provoost, On edge-colouring-games by Erdős, and Bensmail and Mc Inerney, arXiv:2505.03497 (v1 6 May 2025, v2 28 October 2025; carded at its library home). Proposition 9 of v2 (Proposition 10 of v1): Bob wins the unbiased clique game $\mathrm{Clique}(n)$ on $K_n$ for every $3\le n\le8$, and if Alice wins $\mathrm{Clique}(n)$ for some $n\ge8$ then Bob wins $\mathrm{Clique}(n+3)$. The small cases were decided by the authors' exhaustive game solver, an implementation of Zermelo's backward induction over canonically labeled colored graphs (Section 6), with an independent second implementation agreeing for $n\le7$. Table 1 of the same paper gives the optimal outcomes $(a,b)$ of the maximum-degree game (the paper's Star game, outcome $\mathrm{out}_\Delta$) on $K_n$ for $2\le n\le8$: $(1,0)$ on $K_2$ and $(2,1)$ on $K_3$, where Alice wins, and the ties $(2,2)$, $(3,3)$, $(4,4)$, $(4,4)$ and $(5,5)$ on $K_4$ to $K_8$, where Bob, who needs only to prevent Alice's maximum degree from exceeding his, wins. The paper's Conjecture 7 extends the pattern: except for $K_2$ and $K_3$, the Star game on every regular graph is a second-player win.

Covers. Finitely many instances of two questions of Problem 778. The first question (does Bob win the unbiased clique game for $n\ge3$?) has the answer yes for $3\le n\le8$. The third question (who wins the maximum-degree game?) is determined for $n\le8$: Alice wins for $n=2,3$ and Bob for $4\le n\le8$. Not covered: the first question for $n\ge9$ (the $n\to n+3$ transfer is conditional on an Alice win, which the search did not find), the third question for $n\ge9$, and the second question; the paper's Theorem 8, that the second player wins the biased clique game with bias $1:3$ for every $n\ge4$, and its Theorem 11 on biased maximum-degree games concern variants of the second and third questions with other biases and are not claims on this problem. The claim value answered records a yes to instances of the first question together with a determination of the third.

Depends on. Nothing in this wiki: the results are the authors' own computations.

Acceptance. None recorded. The paper is an unrefereed preprint, the computations rest on the authors' implementations (published with the paper, in C and in Sage, in the repository Algorithmic-Graph-Theory-Group/edge-colouring-games linked above at its commit of 6 May 2025), the site's commentary does not cite the paper, and the site's label is OPEN as of 2026-10-06. The claim stays claimed.