Research Seminar Combinatorics
Next Talk
Thursday, November 17th, 2023 at 14:15 |
A3 SR024 |
Jan Volec (Czech Technical University in Prague) |
On the minimum eigenvalue of regular triangle-free graphs. |
Abstract: Motivated by two well-known conjectures of Erdős on triangle-free graphs, Brandt asked in 1994 whether the smallest eignvalue of an n-vertex d-regular triangle-free graph is at most 4n/25 - d. In this talk, we confirm the conjecture of Brandt in a stonger sense: we show that the smallest eigenvalue of the signless Laplacian of any n-vertex triangle-free graph G is at most 15n/94 < 0.1596n. In particular, if G is d-regular, then its smallest eigenvalue is at most 15n/94 - d. |
Schedule and abstracts 2023/2024
Date | Speaker | Title |
---|---|---|
17.11.2023 |
Jan Volec |
On the minimum eigenvalue of regular triangle-free graphs. |
02.11.2023 |
Yamaan Attwa |
Erdős-Hajnal is true for an infinite family of prime graphs. Part II |
26.10.2023 | Yamaan Attwa (FU Berlin) |
Erdős-Hajnal is true for an infinite family of prime graphs. Part I |
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