| $1.393$ | [KSTZ2025] | Current best upper bound: Xu's $m\le 1.393(n-1)$ bound, as recorded in recent literature, gives $C_{78}\le 1.393$. [KSTZ2025-current-best-special] |exact pinned row| $1.393$ | <a href="#KSTZ2025">[KSTZ2025]</a> | Current best upper bound: Xu's $m\le 1.393(n-1)$ bound, as recorded in recent literature, gives $C_{78}\le 1.393$. <a href="#KSTZ2025-current-best-special">[KSTZ2025-current-best-special]</a> |tracked since 2026-07-24 — no movement seen yet
Lower bound, last-listed row
| $1$ | [FP2011] | Any cycle of length at least five can be drawn as a thrackle, and such a cycle has $\lvert E\rvert/\lvert V\rvert=1$. [FP2011-open-sharp] |exact pinned row| $1$ | <a href="#FP2011">[FP2011]</a> | Any cycle of length at least five can be drawn as a thrackle, and such a cycle has $\lvert E\rvert/\lvert V\rvert=1$. <a href="#FP2011-open-sharp">[FP2011-open-sharp]</a> |tracked since 2026-07-24 — no movement seen yet
Cite this rowBounds Ledger — Conway thrackle constant (78a)
upper bound: $1.393$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $1$ (tracked since 2026-07-24 — no movement seen yet)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/78a.html