graph_coloring

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden. It does usefully disclose that the algorithm is greedy, implicitly signaling the result may not use the minimum number of colors, which is meaningful behavioral context. However, it omits the return shape (a color-per-vertex mapping?), behavior on invalid/self-loop input, and any determinism guarantees, so it is only partially complete.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

A single efficient sentence with the operation and its key constraint front-loaded. Nothing is wasted, though it is terse to the point of omitting usage context, which is a completeness rather than conciseness concern.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple 2-parameter algorithm tool with no output schema and no annotations, the description covers the core operation but leaves gaps: the format of the returned coloring, what happens on malformed edge input, and how it relates to sibling graph tools. Adequate but not fully complete.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so both parameters (vertices count, [u,v] edge pairs) are already documented in the schema. The description reinforces that edges define adjacency ('no adjacent vertices share a color') but adds no syntax or format detail beyond the schema. Baseline 3 applies when the schema does the heavy lifting.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb (color), resource (vertices of an undirected graph), and method (greedy algorithm) with the constraint (no adjacent vertices share a color). This lets an agent distinguish it from siblings like chromatic_number, but it does not explicitly name that sibling or the distinction, so it stops short of a 5.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description states what the tool does but gives no guidance on when to use it versus alternatives such as chromatic_number, bipartite_check, or graph_analyze. No conditions, prerequisites, or exclusions are provided, leaving selection entirely to inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.