Maximal independent set¶
In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
Core Idea¶
Maximal independent set is treated here as the recurring computer science and information systems identity summarized by this source-grounded definition: In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set. has six different independent sets, shown as the red vertices. In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
Scope of Application¶
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Documented setting. The phrase "maximal independent set" is also used to describe maximal subsets of independent elements in mathematical structures other than graphs, and in particular in vector spaces and matroids.
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Definition. For a graph G = (V, E) , an independent set S is a maximal independent set if for v \in V , one of the following is true.
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Definition. N(v) \cap S \neq \emptyset where N(v) denotes the neighbors of v.
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Definition. The above can be restated as a vertex either belongs to the independent set or has at least one neighbor vertex that belongs to the independent set.
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Definition. As a result, every edge of the graph has at least one endpoint not in S .
Clarity¶
A clear use of Maximal independent set names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
Manages Complexity¶
Maximal independent set compresses multiple computer science and information systems details into a stable diagnostic relation. The source shows both the central mechanism—any neighbor to a vertex in the independent set S cannot be in S because these vertices are disjoint by the independent set definition.—and the practical consequence—pROOF: Build a directed version of G by directing each edge to the node with the higher degree (breaking.
Abstract Reasoning¶
- Type the carrier. Identify the computer science and information systems entities to which the claim applies.
- State the relation. Use the source-grounded identity: In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.
- Check operation and conditions. That is, it is a set S such that every pair of vertices in S is connected by an edge and every vertex not in S is missing an edge to at.
Knowledge Transfer¶
Within the home domain. Knowledge about Maximal independent set transfers literally when a new case preserves the same carrier type, relation, and recognition test. The phrase "maximal independent set" is also used to describe maximal subsets of independent elements in mathematical structures other than graphs, and in particular in vector spaces and matroids. For a graph G = (V, E) , an independent set S is a maximal independent set if for v \in V , one of the following is true. Beyond the home domain. No canonical parent is asserted for Maximal independent set.
Neighborhood in Abstraction Space¶
Maximal independent set sits in a crowded region of the domain-specific corpus (36th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Data Structures & Graph Variants (17 abstractions)
Nearest neighbors
- Graph Toughness — 0.89
- Complement graph — 0.89
- Tree Decomposition — 0.88
- Independent set (graph theory) — 0.88
- Clique graph — 0.88
Computed from structural-signature embeddings · 2026-10-08