Hoffman bound in graph theory

Target entity: Hoffman bound in graph theory
Context triple: [Alan Hoffman, notableConcept, Hoffman bound in graph theory]

• A. Alon–Boppana bound
  The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. Turán's theorem
  Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
• D. Erdős–Stone theorem
  The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
• E. Graham–Pollak theorem
  The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hoffman bound in graph theory
Target entity description: The Hoffman bound in graph theory is a spectral bound that uses the eigenvalues of a graph’s adjacency matrix to give an upper limit on the size of its maximum independent set (and related parameters like the chromatic number).

• A. Alon–Boppana bound
  The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. Turán's theorem
  Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
• D. Erdős–Stone theorem
  The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
• E. Graham–Pollak theorem
  The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
• F. None of above. chosen