User:David Eppstein/Gallery

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[edit] Mathematical illustrations

I've placed most of the following mathematical illustrations in the public domain. If you see an illustration I've drawn for one of my other web sites, and want it to be uploaded to the commons for whatever reason, please ask by email: if I upload it myself, it can be more properly licensed, and it's likely that I still have the vectorized source instead of the rasterized version I use for web images.

[edit] Configurations and point-line incidences

Hjelmslev's theorem
The Schläfli double six
The Gray configuration
Non-Desargues configuration
The Möbius–Kantor configuration
Complete quadrangle and dual complete quadrilateral
Desargues' configuration as two mutually inscribed pentagons
No-three-in-line problem
Point sets with fewer than n/2 ordinary lines

[edit] Geometric graph theory

Gabriel graph
Relative neighborhood graph
β-skeleton
Empty regions for the β-skeleton
String graph representation of a planar graph
An Erdős-Diophantine graph
Ageev's 5-chromatic circle graph
A circular-arc graph
A bitonic tour
An intersection graph of rectangles, with boxicity two.
Unit disk graph.
Hadwiger–Nelson problem: 7-coloring of the plane and 4-chromatic unit distance graph. From the junkyard.
A 3-colored triangulation for Fisk's proof of the art gallery theorem. From my WG09 slides.

[edit] Cayley graphs and symmetric graphs

Butterfly network as a multitree
Johnson graph J(5,2)
The Clebsch graph labeled as in a construction for Keller's conjecture
The path formed by the Steinhaus–Johnson–Trotter algorithm
K_3,3 with each of its three color classes drawn as parallel line segments on distinct lines
Edge coloring of a complete graph
The Clebsch graph
Construction of the Clebsch graph from a hypercube
One-crossing drawing of K_3,3
A generalized Petersen graph with only three Hamiltonian cycles
The Shrikhande graph in Lombardi style
The Folkman graph in Lombardi style
The octahedron as pancyclic graph
The odd graph O₄
Pappus graph
Brinkmann graph
3-crossing drawing of the Heawood graph
The Petersen graph and its complement
The Nauru graph drawn as a unit distance graph
The intersection graph of the faces of a cube
Toroidal Nauru graph
Genus-4 Nauru graph
Crown graphs
The Wagner graph
The Petersen graph as a Kneser graph
The Shrikhande graph embedded on a torus.
The Gray graph.
The Folkman graph.
A permutohedron.
The Möbius–Kantor graph as a unit distance graph.
The Möbius–Kantor graph embedded symmetrically on a torus.
The cube-connected cycles of order 3.
The Paley graph of order 9 as a perfect graph.
The Petersen graph as a Moore graph.
Two views of the Möbius ladder graph M₁₆
The De Bruijn graph as a line graph
Three-dimensional binary De Bruijn graph
Paley graph, of order 13, as a circulant
Desargues graph

[edit] Dessins d'enfants

A dessin d'enfant
Transforming a dessin d'enfant into gluing instructions for a Riemann surface
The dessins d'enfants for the Chebyshev polynomials
The dessin d'enfant for the sextic monomial p(x)=x⁶
Two conjugate dessins d'enfants

[edit] Miscellaneous graph theory and graph drawing

Moser spindle as a pseudotriangulation
A planar Lombardi drawing of the Frucht graph
A Hamiltonian cycle in the Dürer graph
A 3-regular 1-connected well-covered graph
3-regular 3-connected well-covered graphs
A well-covered graph
A multigraph that has degree six, edge multiplicity three, and requires nine colors in any edge coloring
A 3-regular planar graph that requires four colors in any edge coloring
Hajós construction
An Apollonian network
Graph toughness
The Frucht graph in Lombardi drawing style
The Chvátal graph in Lombardi style
A block graph
A trivially perfect graph
An apex graph
Robertson's irreducible apex graph
The Petersen family
The Herschel graph
Planar separator for a grid graph
Forbidden minors for branchwidth three
Branch-decomposition
Chvátal graph
A caterpillar tree
Forbidden minors for pathwidth 1
Maximal independent sets
Domination in a product of stars, for Vizing's conjecture
Subdivision of K₅
The Goldner–Harary graph
The Herschel graph
A Halin graph
Forming a Schlegel diagram from shadows and light
The Rado graph
An equitable coloring
A cycle double cover of the Petersen graph
A Fibonacci cube
Finding matchings in claw-free graphs
An augmenting path in a claw-free graph
A simplex graph
A forbidden subgraph for comparability graphs
A factor-critical graph
Thomassen's girth-3 hypohamiltonian graph
A hypohamiltonian graph
Hadwiger's conjecture
A clique-sum
A distance-hereditary graph
Construction of a distance-hereditary graph
An implication graph
The median graph representing the set of solutions to a 2-satisfiability instance
A squaregraph
Converting a triangle-free graph into a median graph.
The Buneman graph, a median graph representing maximum-parsimony evolutionary relationships.
The retraction of a cube onto a median graph.
The median of three vertices in a median graph.
The median of three vertices in a tree.
A cograph described by a cotree.
A forbidden subgraph for the line graphs of hypergraphs
A self-complementary graph
Forbidden minors for partial 3-trees.
A graph and its tree decomposition.
An interval graph.
Partition of the complete bipartite graph K_4,4 into three forests, showing that it has arboricity three.
A functional graph.
The butterfly and diamond, forbidden minors for pseudoforests.
A pseudoforest.
The Erdős–Faber–Lovász conjecture.
A 4x4 grid graph and one of its spanning trees.
Fáry's theorem, induction step of proof
An aperiodic graph.
A graph that is not aperiodic as all cycles are divisible by three.
The Turán graph T(13,4).
Thue number of the 5-cycle is four
Wheel graphs with 4 to 9 vertices.
Beineke's nine forbidden line graphs.
Series-parallel graph.
Split graph.
The rooted product of graphs.
The lexicographic product of graphs.
The tensor product of graphs.
The cartesian product of graphs.
Partition of the torus into seven mutually adjacent regions, for Heawood conjecture.
Cactus graph
The Grötzsch graph.
König's theorem proof
König's theorem example
Erdős–Gyárfás conjecture, Markström's 4- and 8-cycle-free graph
The Grötzsch graph as the Mycielskian of a 5-cycle graph.

[edit] Miscellaneous geometry

Compound of three octahedra
Automedian triangle
Subdivisions of a pentagon
An orthodiagonal quadrilateral
British flag theorem
Pythagorean dissections
Similarity tiling by Koch snowflakes
Aperiodic section of the Pythagorean tiling
Tiling of the plane by shifted squares
Nearest neighbor graph
Theil–Sen estimator
Kawasaki's theorem
Midsphere
Inner radius
Shapley–Folkman lemma
Skew lines on nested hyperboloids
Tverberg's theorem
Radon's theorem
Helly's theorem
The Hadwiger conjecture in combinatorial geometry
The Schönhardt polyhedron.
A cube dissected into orthoschemes.
A Davenport–Schinzel sequence from a lower envelope of line segments
The Fermat–Apollonius circle of an ellipse.
The trisected perimeter point of a 3-4-5 right triangle.
Four levels of the Z-curve
Z-curve via interleaved binary coordinates
The Brocard point of a triangle
Intersecting planes
Chao's characterization of tangential quadrilaterals
A tangential quadrilateral
Convex layers and a halfspace. For an example in fractional cascading.
A Vietoris–Rips complex.
Happy Ending problem, eight points with no pentagon
Orthogonal convex hull and tight span.
Pseudotriangles.
The Szilassi polyhedron. From the junkyard.
A point quadtree.
The face lattice of a square pyramid.
The Nagel point of a triangle.
The Philo line and its application to doubling the cube.
Heesch's problem, Amman's dented hexagon. From the junkyard.
Convex shelling.
Happy Ending problem, quadrilaterals in five-point sets.
Pitteway triangulation
K-sets
H tree
Erdős–Szekeres theorem, geometric interpretation as monotone path

[edit] Number theory

Stella octangula number
Representation of octahedral numbers as centered square pyramids
Octahedral number
Squares in a square
Calkin–Wilf sequence
Calkin–Wilf tree
15=4+5+6 is a polite number
Dyadic rationals
Graphical demonstration of a solution to Znám's problem.
Graphical demonstration that 1 = 1/2 + 1/3 + 1/7 + 1/43 + ...; see Sylvester's sequence.
Square pyramidal number.
Rational approximations to the octagon from Pell numbers.
Integer right triangles with nearly-equal legs from Pell numbers.
Divisibility of regular numbers.

[edit] Order theory

Dedekind–MacNeille completion
A fence
The extreme case for the 1/3–2/3 conjecture
A series-parallel partial order
A semiorder
Free distributive lattice of monotonic Boolean functions.
Young–Fibonacci lattice.
Young's lattice.
Example for Birkhoff's representation theorem.
A Tamari lattice.
The Hasse diagram of a distributive lattice.
Dilworth's theorem, transformation from chain decomposition to bipartite matching.
The 13 possible strict weak orderings on a set of three elements.
A partial order of dimension 4 and its realizer.
The lattice of subgroups of Dih₄.
A concept lattice.
Three views of an antimatroid.

[edit] Cellular automata

Rule 90 gate array
Trees in Rule 90
Critters
Block cellular automaton
Day & Night, Bell's p256 butterfly gun
One-dimensional cyclic cellular automaton.
Two-dimensional cyclic cellular automaton.
puffer train.
The space rake.
Rule 184 as a model of traffic flow.
Rule 184 as a model of deposition.
Rule 184 as a model of ballistic annihilation.
Rule 184

[edit] Algorithms and data structures

Prefix sum
An SPQR tree.
Consecutive pairs that bracket x in a sequence, for the Cartesian tree article
A Cartesian tree
Using a Cartesian tree for range searching
Johnson's algorithm
Floyd's "tortoise and hare" cycle detection algorithm.
Bloom filter

[edit] Miscellaneous

Combinatorial equivalence between plane trees, polygon subdivisions, and parenthesizations
A Langford pairing
Pitch class space
Descriptive chess notation
Binary erasure channel
Binary symmetric channel
Diagram for a triangulated category
academic genealogy of Johannes De Groot and his namesake
A train track on a triple torus.
A switch in a train track.

[edit] Photography

Most of my photos here are licensed under Creative Commons Attribution Share-Alike. See Flickr for some of my other photos, and my web site for almost all of them; if it's not listed here, it's probably not yet publically licensed, but I may be willing to share anyway.