Question

The 2004 proof that “SL = L” used one of these objects that was constructed using the zig-zag product. A “phase transition” at a critical probability value characterizes the study of these mathematical objects in percolation theory. The Erdős–Rényi model describes randomized examples of these objects. The size of an independent set of one of these objects (10[1])can be bounded by (-5[1])the maximum eigenvalue of its Laplacian matrix (10[1])or the size of its adjacency matrix. Determining (10[1])if one of these objects is triangle-free has important implications (10[1])for computing its chromatic number. These objects (10[1])only contain even cycles if and only if they are bipartite. For 10 (10[1])points, name these mathematical objects that contain vertices and edges, (10[1]-5[1])which are often used to model networks. ■END■ (10[1]0[2])

ANSWER: graphs [accept specific types of graphs such as random graphs or expander graphs or undirected graphs or directed graphs or bipartite graphs; prompt on networks until read]
<Other Science>
= Average correct buzz position

Back to tossups

Summary

2024 ACF Winter at Clemson2024-11-16Y989%0%22%89.75
2024 ACF Winter at Ohio State2024-11-16Y1100%0%0%66.00

Buzzes

PlayerTeamOpponentBuzz PositionValue
Bharath RamGeorgia Tech DGeorgia Tech A5610
TurjyaGeorgia AAuburn C60-5
Rohan DalalGeorgia Tech BGeorgia Tech F6710
Cole WelchGeorgia Tech EGeorgia A7510
Arunn SankarGeorgia Tech CTennesse B8510
Parker McCoigTennesse AAuburn C9210
Coy MierAuburn CGeorgia A10510
Asheton WilbanksClemson ASouth Carolina A115-5
Malachi LedfordTusculum AEmory B11510
Jackson McDonaldAlabama AAuburn B1230
TJ PickeringAuburn BAlabama A1230
Caleb SlusherSouth Carolina AClemson A12310