chromatic_number

std.linalg.chromatic_number · Level L3

The chromatic number χ(G) of a finite undirected simple graph with at least one vertex, and a proper colouring with χ(G) colours: k_colorable for k = 1, 2, …, until one succeeds. Each failure is a complete search, so the answer is exact; a greedy colouring is only an upper bound. A graph with no edges has χ = 1.

χ(G) = min{k : G is k-colourable}

Signature

chromatic_number(A: f64[n, n]) → f64[], f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the first k for which the backtracking search succeeds in exact rational arithmetic, on all 40 test cases.
All 163 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

chromatic_open chromatic_step

Called by

—

sha256:08fe28890b2c943c1066ee7151d78215560c43f64cb0607a733b3c278bcfa4f3

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.chromatic_number · Ω:chromatic_number
Pins: sha256:68eee5be4eb55d90bd217af59491dc7066e6edb1c3d2f3eca15e90eb3805f656this graph and the 5 it reaches through calls
Evidence: sha256:f31358e34697ba9390a155474035261eb2ee6d76e4ae029596128795bad79fd2the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.