NP-complete problems

, abbreviated or , is a binary-determination logic puzzle published by Nikoli. A book consisting entirely of puzzles has been published by Nikoli.

thumb|upright=1.3|SameGame for Mac, by Takahiro Sumiya is a tile-matching puzzle video game originally released under the name CHAIN SHOT in 1985 by Kuniaki "Morisuke" Moribe. It has since been ported to numerous computer platforms, handheld devices, and even TiVo, with new versions as of 2016.

the smallest number of edge crossings possible in a drawing of a node-link graph

a sequence of operations for computing a given integer by summing smaller integers

classic computing problem

Numberlink is a type of logic puzzle involving finding paths to connect numbers in a grid.

graph coloring in which each color pair is represented by an edge of the graph

thumb|A Heyawake puzzle Heyawake (Japanese: へやわけ, "divided rooms") is a binary-determination logic puzzle published by Nikoli. As of 2013, five books consisting entirely of Heyawake puzzles have been published by Nikoli. It first appeared in Puzzle Communication Nikoli #39 (September 1992).

graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point with a single additional edge

In graph theory, a path decomposition of a graph is, informally, a representation of as a "thickened" path graph, and the pathwidth of is a number that measures how much the path was thickened to form . More formally, a path-decomposition is a sequence of subsets of vertices of such that the endpoints of each edge appear in one of the subsets and such that each vertex appears in a contiguous subsequence of the subsets, and the pathwidth is one less than the size of the largest set in such a decomposition. Pathwidth is also known as interval thickness (one less than the maximum clique size

Concept in mathematical graph theory

a subset of the edges in a directed graph that includes at least one edge from each cycle

minimum number of planar graphs into which the edges can be partitioned

disjoint family of sets, drawn from a larger collection, with the same union as the whole collection

intersection graph of unit disks in the plane

In the mathematical field of graph theory, the boxicity of a graph is a graph invariant defined to be the minimum dimension of Euclidean space required to represent the graph as an intersection graph of axis-parallel closed boxes. That is, there must exist a one-to-one correspondence between the vertices of the graph and these boxes, such that two boxes intersect if and only if there is an edge connecting the corresponding vertices.

graph invariant

thumb|upright=1.35|Branch decomposition of a grid graph, showing an e-separation. The separation, the decomposition, and the graph all have width three. In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves. Removing any edge from T partitions the edges of G into two subgraphs, and the width of the decomposition is the maximum number of shared vertices of any pair of subgraphs formed in this way. The branchwidth of G is the minimum width of any branch-decomposi

Biclustering, block clustering,

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graph theory