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SQUAREGRAPH

Squaregraph

Planar graph with quadrilateral faces

In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded

Squaregraph

King's graph

Graph of king moves on a chessboard

generalization of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph in which each bounded face is a quadrilateral and each

King's graph

King's_graph

Matchstick graph

Graph with edges of length one, able to be drawn without crossings

arbitrary tree as a matchstick graph. A similar property is true for squaregraphs, the planar graphs that can be drawn in the plane in such a way that

Matchstick graph

Matchstick_graph

Median graph

Graph with a median for each three vertices

such a way that medians can be calculated coordinatewise in this way. Squaregraphs, planar graphs in which all interior faces are quadrilaterals and all

Median graph

Median_graph

List of graphs

Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. Gear graphs are also known as

List of graphs

List_of_graphs

Bipartite graph

Graph divided into two independent sets

even length is bipartite. Special cases of this are grid graphs and squaregraphs, in which every inner face consists of 4 edges and every inner vertex

Bipartite graph

Bipartite_graph

Polyomino

Geometric shape formed from squares

representations of the symmetric group. Blokus, a board game using polyominoes. Squaregraph, a kind of undirected graph including as a special case the graphs of

Polyomino

Glossary of graph theory

subgraph of its square induced by one side of the bipartition. 2. A squaregraph is a planar graph that can be drawn so that all bounded faces are 4-cycles

Glossary of graph theory

Glossary_of_graph_theory

Circle graph

Intersection graph of a chord diagram

triangle-free circle graphs is equivalent to the problem of representing squaregraphs as isometric subgraphs of Cartesian products of trees; in this correspondence

Circle graph

Circle_graph

Partial cyclic order

Eppstein, David (2010), "Combinatorics and geometry of finite and infinite squaregraphs" (PDF), SIAM Journal on Discrete Mathematics, 24 (4): 1399–1440, arXiv:0905

Partial cyclic order

Partial_cyclic_order

Penny graph

Graph formed by touching unit circles

By arranging the pennies in a square grid, or in the form of certain squaregraphs, one can form triangle-free penny graphs whose number of edges is at

Penny graph

Penny_graph

Partial cube

Isometric subgraph of a hypercube

graphs are examples of median graphs. Since the median graphs include the squaregraphs, simplex graphs, and Fibonacci cubes, as well as the covering graphs

Partial cube

Partial_cube