Complete graph
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Six people at a party
Among any six people, three are mutual acquaintances or three are mutual strangers. Five is not enough, and the arrangement that saves five is a pentagon. Beyond that the numbers become unknowable.
A walk that changes one thing at a time
Counting from nothing to fifteen in binary changes four digits at once somewhere in the middle. There is another order through the same sixteen words in which every step changes exactly one — and it is a closed walk on a four-dimensional cube.
Named alongside it
The objects these essays reach for when they reach for this one.
Counting argumentGraphParityBinaryExistence proofGray codeHamming distanceHypercubeKarnaugh mapNonconstructivePigeonhole principleProbabilistic method