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. In other words...

Independent sets have also been called "internally stable sets", of which "stable set" is a shortening. A maximal independent set is an independent set...

Dominating sets are closely related to independent sets: an independent set is also a dominating set if and only if it is a maximal independent set, so any...

a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent set. As an example,...

each color class one at a time. It does this by identifying a maximal independent set of vertices in the graph, assigning these to the same color, and...

property that any maximal clique intersects any maximal independent set in a single vertex. An interval graph is a graph whose maximal cliques can be ordered...

Alternatively, (1) a maximal independent set is a dominating set, and (2) the complement of a maximal independent set is also a dominating set if there are no...

planar graphs while the independent set problem remains NP-hard on planar graphs. A maximal clique, sometimes called inclusion-maximal, is a clique that is...

each color class one at a time. It does this by identifying a maximal independent set of vertices in the graph using specialised heuristic rules. It...

proving bounds on a circular maximal function analogous to the Kakeya maximal function. It was conjectured that there existed sets containing a sphere around...

which are adjacent to each other; an independent set is maximal if it is not a subset of a larger independent set. In any graph, the "heavy" vertices that...

Equivalently, well-covered graphs are the graphs in which all maximal independent sets have equal size. Well-covered graphs were defined and first studied...

claw-free graph. Every maximal independent set in a cluster graph chooses a single vertex from each cluster, so the size of such a set always equals the number...

contains at least one maximal element. The lemma was proved (assuming the axiom of choice) by Kazimierz Kuratowski in 1922 and independently by Max Zorn in 1935...

dominating set of size at most k and computes a maximal independent set of Gi, looking for the smallest index i that has a maximal independent set with a...

whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single vertex. A cograph is a graph in which...

that is not independent is called dependent. A maximal independent set – that is, an independent set that becomes dependent upon adding any element of...

running times that are, in theory, better on inputs that have few maximal independent sets, the Bron–Kerbosch algorithm and subsequent improvements to it...

problem: GT49  Maximum independent set: GT20  Maximum Induced path: GT23  Minimum maximal independent set a.k.a. minimum independent dominating set NP-complete special...

Min vertex cover. The complement of any maximal independent set must be a vertex cover. Min dominating set in bounded-degree graphs. The travelling salesman...

Feistel cipher construction. His distributed algorithm to find a maximal independent set in a computer network has also been influential. Luby received...

graph, meaning that every maximal independent set has the same size. In this graph, the only two maximal independent sets are the two sides of the bipartition...

{\displaystyle C} . In this way, C {\displaystyle C} becomes a maximal independent set among the vertices that were not already assigned smaller colors...

matrix-chain multiplication problem max-heap property maximal independent set maximally connected component Maximal Shift maximum bipartite matching maximum-flow...

the size of its independent sets. An intersecting family of r {\displaystyle r} -element sets may be maximal, in that no further set can be added (even...

graph is a graph in which every induced subgraph has an independent set meeting all maximal cliques. The Meyniel graphs are also called "very strongly...

information system Marine isotope stage, stages of the Earth's climate Maximal independent set, in graph theory Metal-insulator-semiconductor, e.g., in MIS capacitor...

an independent set) or all vertices have strictly less than ⌊ n ⌋ {\displaystyle \lfloor {\sqrt {n}}\rfloor } neighbors (in which case any maximal independent...

algebra to determine a maximal independent set among these eta quotients. Assuming that we have not already found D linearly independent eta quotients, find...

Distributed Computing Schneider, J. (2008), "A log-star distributed maximal independent set algorithm for growth-bounded graphs" (PDF), Proceedings of the...