The list balancing number always exists, coincides with the balancing number when the latter does, and is exactly determined for cycles except 4k-cycles (tight bounds) with general bounds via extremal numbers and a surprisingly large value for K5.
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The balancing number and list balancing number of some graph classes
The list balancing number always exists, coincides with the balancing number when the latter does, and is exactly determined for cycles except 4k-cycles (tight bounds) with general bounds via extremal numbers and a surprisingly large value for K5.