Description
Return unpaired vertices from a supplied matching size.
Graph and lattice counts depend on the allowed moves, edges and geometric or incidence assumptions. A necessary count identity or local conflict test may hold even when no valid complete object with the requested structure has been supplied.
Return unpaired vertices from a supplied matching size.
When to use this tool
Use Matching Unpaired Vertex Budget when checking one supplied path, tree, matching or rook-placement condition.
How to use the tool and how it works
- Enter vertices, edges. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read unpaired. Use the output convention below.
Return unpaired vertices from a supplied matching size. Require whole vertices >= 0 and edges in [0,floor(vertices/2)]; unpaired = vertices-2*edges.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 0. |
| edges | Edges | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| unpaired | Unpaired | Required. Safe integer. |
{
"input": {
"vertices": 9,
"edges": 3
},
"output": {
"unpaired": 3
}
}Limitations and assumptions
- The count assumes disjoint matching edges; no actual graph, matching validity or maximum matching is computed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Inspect or construct the complete graph/path and apply all relevant structural constraints for a full validity or counting result.
References
Similar or alternative tools
- Hypergraph Uniform Edge Incidence Count
Return incidence count of a uniform hypergraph.
- Catalan Triangulation Diagonal Budget Tool
Calculate catalan triangulation diagonal budget from explicit caller-supplied inputs.