is_bicriticalCheck whether a graph is bicritical by verifying that deleting any two distinct vertices still leaves a perfect matching.
Is the graph bicritical: does G - u - v have a perfect matching for every pair of distinct vertices u, v?
| Name | Required | Description | Default |
|---|---|---|---|
| graph | Yes | a graph6 string or a registry name. |
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||
Changes observed during successful MCP inspections.
v0.1.0Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the behavioral disclosure burden. It fully specifies the tested condition, including the requirement for every distinct vertex pair and perfect matching existence, which is strong transparency for a predicate tool.
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?
The description is a single efficient sentence that states the property precisely and front-loads the main purpose. Every part of the sentence earns its place with no redundancy or filler.
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 one-parameter predicate with a fully documented schema and an output schema available, the description is complete enough. It provides the exact mathematical semantics needed to invoke the tool correctly and interpret its result.
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?
The schema already documents the graph parameter at 100% coverage, so the baseline is 3. The description adds useful context about how the graph is interpreted in the bicritical condition, but it does not add new parameter-level format or usage details beyond the schema.
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?
The description clearly states the tool checks whether a graph is bicritical and defines the condition in mathematical terms. It lacks an explicit contrast with sibling tools like is_brick or is_matching_covered, but the verb and resource are unambiguous.
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 definition implies the tool is for determining bicriticality, but it does not state when to prefer it over related predicates such as is_brick or is_matching_covered, nor does it mention any exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.