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In a list (d1,…,dn) of positive integers, let r and s denote the largest and smallest entries. A list is gap-free if each integer between r and s is present. We prove that a gap-free list with even sum is graphic if it has at least r+r+s+12s terms. With no restriction on gaps, length at least (r+s+1)24s suffices, as proved by Zverovich and Zverovich (1992). Both bounds are sharp within 1. When the...
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