Summary

dsatur_coloring tracks the highest assigned color in max_color and returns max_color + 1 as the number of used colors.

When the input graph is empty, no node is ever colored, max_color stays at its sentinel value, and the function still returns 1. And yet, an empty graph uses zero colors.

Expected behavior

The color count should be 0 when no node was colored.

Concrete regression test

use petgraph::{Graph, Undirected, algo::dsatur_coloring};

#[test]
fn dsatur_coloring_empty_graph_uses_zero_colors() {
    let graph: Graph<(), (), Undirected> = Graph::new_undirected();

    let (coloring, nb_colors) = dsatur_coloring(&graph);

    assert!(coloring.is_empty());
    assert_eq!(nb_colors, 0);
}

This currently fails because dsatur_coloring(&graph) returns (empty_map, 1) for an empty graph.

Suggested fix

Special-case the empty graph or derive the count from whether any color assignment actually happened.