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The bound $O(n^{1-\epsilon/\alpha})$ on the additional number of edges for $0<\epsilon<\alpha$ is asymptotically tight at the two extremities of the interval $(0,\alpha]", and has implications to the design of graphs with minimum broadcast cost, defined as number of edges times broadcast time.
It is shown that there are infinitely many locally checkable problems (i.e., problems whose solutions can be checked locally) whose round complexities belongs to the two intervals $[omega(1),o(\log\log^\star n)]$ and $[\omega(\log^\star n),o(\log n)] whenever these problems are considered in networks with unbounded max...
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