The 1-2-3 conjecture… to The Balister–Győri–Schelp…
- The 1-2-3 conjecture (Karoński–Łuczak–Thomason 2004; proved by Keusch 2024)
- Reed's omega, delta, and chi conjecture
- Ringel's Conjecture
- Shelah-Spencer's Zero-One Law for Sparse Random Graphs
- Size, Order, and Connected Domination
- Tu-Deng Conjecture
- The length of an \(s\)-increasing sequence of \(r\)-tuples
- Ringel's Conjecture and Kotzig's Conjecture for large \(n\)
- Barker sequences
- Independent Domination of Regular Graphs, Conjecture 1.6
- Digit \(2\) in base \(3\) representation of \(2^n\)
- TxGraffiti Conjecture 1: independence, annihilation, and residue
- TxGraffiti Conjecture 2: zero forcing versus independence (cubic graphs)
- TxGraffiti Conjecture 3: independent domination versus saturation (regular)
- TxGraffiti Conjecture 4: the saturation number versus the harmonic index
- First Proof, Theorem 6
- Dean's conjecture on cycles of length divisible by `k`
- Bondy's conjecture on longest cycles in highly connected graphs
- The Alon-Tarsi short cycle cover conjecture
- The Balister–Győri–Schelp conjecture
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