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edge-addition monotonicity

topic1 events
papersTODAY 04:00 UTC

Positive p-energy edge-addition monotonicity found to fail for all p >= 1

A conjecture raised by Guo at a 2021 AIM workshop proposed that the positive square energy s+ = E+_2 would behave like the spectral radius, never dropping when an edge is added to a graph. That claim was later disproven for the case p = 2. A new arXiv preprint by Tang, Liu and colleagues establishes that edge-addition monotonicity fails for every p >= 1.

graph-theory/spectral-graph-theory/mathematics/research