We study exclusion zones for instant-runoff voting (IRV) on connected, unweighted graphs. Each vertex hosts one voter and may host a candidate. Voters rank candidates by shortest-path distance and cast one whole vote in each round. Distance ties favour the smaller identifier in a common fixed vertex ordering, and equal-score elimination ties remove the larger identifier in that ordering. A nonempty vertex set $S$ is an exclusion zone if every election with at least one participating candidate in $S$ elects a winner in $S$. In this setting, we consider three computational problems: deciding whether a target candidate can lose against some nonempty subset of a given set of allowed opponents, deciding whether a given vertex subset is an exclusion zone, and computing the unique minimum exclusion zone. We establish that all three are polynomial-time solvable on trees, outerplanar graphs and, more generally, planar graphs. For an n-vertex tree, the first problem (candidate loss) can be decided in O(n) time. The planar algorithm uses the structure of an inclusion-minimal candidate set that eliminates the target in the first round: contracting the candidates' voter cells makes the target cell adjacent to every other cell, leading to bounded-width structure and enumerable separators. We give explicit implementations and conservative polynomial running-time and space bounds; the large exponents for outerplanar and planar graphs establish tractability rather than practical efficiency. In contrast, even on bipartite exact one-apex graphs of bounded diameter with every nontarget vertex eligible to stand, candidate loss is NP-complete, singleton-zone verification is coNP-complete, and the minimum exclusion zone cannot be computed in polynomial time unless P = coNP. Thus planarity marks a tractability boundary for these computational problems under the voting and tie-breaking conventions studied here.

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