{"schema":"vela.problem-packet.v0.1","problem":82,"statement":"Let $F(n)$ be maximal such that every graph on $n$ vertices contains a regular induced subgraph on at least $F(n)$ vertices. Prove that $F(n)/\\log n\\to \\infty$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A120414","name":"a(0)=0, a(1)=1; thereafter a(n) = ceiling((3/2)^(n-3)*n*(n-1)).","terms":"0,1,2,6,18,45,102,213,426,821,1538,2820,5075,8996,15743,27247,46709,79405,133996,224640,374400,620715,1024180,1682580,27","url":"https://oeis.org/A120414"},{"id":"A390256","name":"Minimum size of maximum clique or independent set of a graph on n vertices.","terms":"0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4","url":"https://oeis.org/A390256"},{"id":"A390257","name":"Minimum size of maximum regular induced subgraph of a graph on n vertices.","terms":"0,1,2,2,2,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5","url":"https://oeis.org/A390257"},{"id":"A390919","name":"Number of graphs with n vertices that have no induced regular subgraph of order 5 or greater.","terms":"1,2,4,11,31,130,728,6027,66308,818276,8336902,45933753,79888458,23814804,512906,954,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,","url":"https://oeis.org/A390919"},{"id":"A392636","name":"Number of graphs with n vertices that have no induced regular subgraph of order 6 or greater.","terms":"1,2,4,11,34,148,960,10390,188560,5317230,202396620,8905369148,384098286140,13129756210164","url":"https://oeis.org/A392636"},{"id":"A394400","name":"Number of graphs with n vertices that have no induced regular subgraph of order 4 or greater.","terms":"1,2,4,7,11,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,","url":"https://oeis.org/A394400"},{"id":"A394462","name":"Number of graphs with n vertices that have no induced regular subgraph of order 6.","terms":"1,2,4,11,34,148,964,10472,191776,5524670,219302174,10333796899,493296884096,19658348081642","url":"https://oeis.org/A394462"},{"id":"A394539","name":"Number of graphs with n vertices that have no induced regular subgraph of order 5.","terms":"1,2,4,11,31,136,792,7185,94893,1714430,37216434,854671213,18369802688,328662169364,4236467418682,29440587191035,80145694","url":"https://oeis.org/A394539"},{"id":"A394563","name":"Least integer a(n) such that every graph on a(n) vertices has an induced regular subgraph of order at least n.","terms":"1,2,5,7,17","url":"https://oeis.org/A394563"},{"id":"A394564","name":"Least integer a(n) such that every graph on a(n) vertices has an induced regular subgraph of order n.","terms":"1,2,6,8,21","url":"https://oeis.org/A394564"},{"id":"A394573","name":"Number of graphs with n vertices that have no induced regular subgraph of order 4.","terms":"1,2,4,7,12,12,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,","url":"https://oeis.org/A394573"},{"id":"A394574","name":"a(n) is the greatest k such that every graph on n vertices has an induced regular subgraph of order k.","terms":"0,1,2,2,2,2,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5","url":"https://oeis.org/A394574"},{"id":"A394930","name":"Number of graphs with n vertices that have no induced regular subgraph of order 7.","terms":"1,2,4,11,34,156,1038,12246,269646,11453460,907948002,127924347122,30302185606487","url":"https://oeis.org/A394930"},{"id":"A394933","name":"Number of graphs with n vertices that have no induced regular subgraph of order 7 or greater.","terms":"1,2,4,11,34,156,1038,12226,268920,11361262,885194426,119298229792,25716285392622","url":"https://oeis.org/A394933"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}