Perfect matching
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The symmetric graphs no tour can close
Take the words of five places with two ones and join two when they share no one. The ten words look exactly alike to the graph, and no closed tour runs through them — because every way of leaving out one edge at each word leaves two pentagons. Only four connected graphs this symmetric are known to fail like that, and nobody knows whether a fifth exists.
The roots every matching polynomial keeps real
Count a graph's matchings by size and make the counts the coefficients of a polynomial. On every one of 35,664 graphs tested, that polynomial has only real roots — a theorem of Heilmann and Lieb from 1972. Count independent sets instead and the roots wander off the axis on a growing share of graphs, but never on a graph without a claw, and matchings are the independent sets of a graph that never has one.
Named alongside it
The objects these essays reach for when they reach for this one.
Fano planeGenerating functionHamiltonian cycleIndependent setInterlacingKneser graphLog-concavityPetersen graphReal rooted polynomialVertex-transitive