# User:David Eppstein/Gallery

See me on Wikipedia.

## Mathematical illustrations[edit]

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.

### Configurations and point-line incidences[edit]

Non-Desargues configuration

Complete quadrangle and dual complete quadrilateral

Desargues configuration as two mutually inscribed pentagons

Point sets with fewer than n/2 ordinary lines

### Geometric graph theory[edit]

Grid bracing and its graph-theoretic analysis

Flexibility of an unbraced square grid in the grid bracing problem

Greedy geometric spanner with distance ratio 1.1

Greedy geometric spanner with distance ratio 2

The smallest cubic matchstick graph

Integral Fáry embedding of the octahedron

Slope number of the Petersen graph

Slope number of bounded-degree planar graphs

Empty regions for the β-skeleton

String graph representation of a planar graph

Ageev's 5-chromatic circle graph

An intersection graph of rectangles, with boxicity two.

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.

### Cayley graphs and symmetric graphs[edit]

The Johnson graph

*J*(4,2)The smallest zero-symmetric graph with only two edge orbits

The graph of the 3-3 duoprism

*K*_{5}subdivision of a crown graph illustrating the Kelmans–Seymour conjecturedistinguishing coloring of a hypercube

1-planar 8-crossing Nauru graph

Hamiltonicity of the truncated octahedral graph

18-vertex zero-symmetric graph

12-vertex crown graph

*K*_{5}and*K*_{3,3}as minors of the Petersen graph*K*_{2,2,2,2}as a 1-planar graphButterfly 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

Edge coloring of a complete graph

The Clebsch graph

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

*O*_{4}3-crossing drawing of the Heawood graph

The Petersen graph and its complement

The Nauru graph drawn as a unit distance graph

Toroidal Nauru graph

Genus-4 Nauru graph

The Petersen graph as a Kneser graph

The Shrikhande graph embedded on a torus.

The Gray graph.

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

*M*_{16}The De Bruijn graph as a line graph

Three-dimensional binary De Bruijn graph

Paley graph, of order 13, as a circulant

### Dessins d'enfants[edit]

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)=x

^{6}Two conjugate dessins d'enfants

### Miscellaneous graph theory and graph drawing[edit]

A graph of cutwidth 2

A bipartite graph and its line graph

Complementary perfect graphs

The Fritsch graph and its dual map

26-fullerene graph with distance labels

Unit distance graph with 16 vertices and 40 edges

Tree with 480 symmetries, example for Jordan–Pólya number

3-colorings of a path graph

Hamiltonian path in the Herschel graph

Medial graph of the Herschel graph

Example for Grötzsch's theorem

The densest possible planar locally linear graphs

Illustration for the proof of Ore's theorem

Hamiltonian cycle in which nonadjacent pairs of vertices have degrees summing to at least

*n*, for Ore's theoremLombardi drawing of the Golomb graph

Graphic matroid parity

Tangled Kempe chains in the Errera graph

Tangled Kempe chains in the Poussin graph

Clique-width construction

A Halin graph without any 8-cycles

Bidirected graph features

A 2-degenerate graph and its 2-core

Tietze's graph on a Möbius strip

Partition of a line graph into cliques

A bramble in a 3x3 grid graph

List coloring for

*K*_{3,27}Moser spindle as a pseudotriangulation

A planar Lombardi drawing of the Frucht graph

A Hamiltonian cycle in the Dürer 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

The Frucht graph in Lombardi drawing style

The Chvátal graph in Lombardi style

An apex graph

The Petersen family

The Herschel graph

Planar separator for a grid graph

Forbidden minors for branchwidth three

Domination in a product of stars, for Vizing's conjecture

Subdivision of

*K*_{5}The Herschel graph

Forming a Schlegel diagram from shadows and light

The Rado graph

A cycle double cover of the Petersen graph

Finding matchings in claw-free graphs

An augmenting path in a claw-free graph

A forbidden subgraph for comparability graphs

Construction of a distance-hereditary graph

The median graph representing the set of solutions to a 2-satisfiability instance

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.

A cograph described by a cotree.

A forbidden subgraph for the line graphs of hypergraphs

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.The butterfly and diamond, forbidden minors for pseudoforests.

A pseudoforest.

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.

Partition of the torus into seven mutually adjacent regions, for Heawood conjecture.

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.

### Miscellaneous geometry[edit]

Illustration for a proof of the Erdős–Anning theorem

16 polygonalizations of a set of six points

Planar double bubbles

Crease pattern for Schwarz lantern

Empty regions for the Euclidean minimum spanning tree

Opaque forests for a circle

Collinear form of Cairo pentagonal tiling

Equilateral form of Cairo pentagonal tiling

Reuleaux triangle and its middle hedgehog

Curve of constant width based on a semi-ellipse

Tresillo rhythm as a polygon

Curve-shortening of a convex curve

Visual proof of Balinski's theorem

Non-convex pentagonal tiling

Non-convex pentagonal tiling

The Reuleaux triangle in a cluster of four soap bubbles

Heesch's anisohedral tiling

89th stage of toothpick sequence

Overlaid Pythagorean tilings

Coloring argument for De Bruijn's theorem

Non-harmonic packing for De Bruijn's theorem

Circles meeting at the isodynamic point

Construction of the isodynamic point

Similarity tiling by Koch snowflakes

Aperiodic section of the Pythagorean tiling

Skew lines on nested hyperboloids

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

Convex layers and a halfspace. For an example in fractional cascading.

Happy Ending problem, eight points with no pentagon

The Szilassi polyhedron. From the junkyard.

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.

Happy Ending problem, quadrilaterals in five-point sets.

Erdős–Szekeres theorem, geometric interpretation as monotone path

### Number theory and combinatorics[edit]

Gomory's theorem on domino tiling mutilated chessboards

Growth rate of the Moser–de Bruijn sequence

Addition of numbers in the Moser–de Bruijn sequence

A cap set

Bijection between binary trees and stack-sortable permutations

Lower bound construction for the Erdős–Ko–Rado theorem

Trees counted by the Wedderburn–Etherington numbers

Dickson's lemma applied to the hyperbola

*xy*≥ 9Trees counted by the ordered Bell numbers

15=4+5+6 is a polite number

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.

Rational approximations to the octagon from Pell numbers.

Integer right triangles with nearly-equal legs from Pell numbers.

Divisibility of regular numbers.

### Order theory[edit]

2-dimensional modular lattice

A fence

The extreme case for the 1/3–2/3 conjecture

Example for Birkhoff's representation theorem.

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 Dih

_{4}.Three views of an antimatroid.

### Cellular automata[edit]

Critters transition rule

Rule 90 gate array

Trees in Rule 90

Day & Night, Bell's p256 butterfly gun

One-dimensional cyclic cellular automaton.

Two-dimensional cyclic cellular automaton.

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.

### Algorithms and data structures[edit]

An SPQR tree.

Using a Cartesian tree for range searching

Floyd's "tortoise and hare" cycle detection algorithm.

### Topology[edit]

Symmetric Whitehead link

Six-component "rubberband" Brunnian link

Algebraic link diagram for the Borromean rings

Trefoil with bridge number 2

A train track on a triple torus.

A switch in a train track.

### Miscellaneous[edit]

Diagram for a triangulated category

academic genealogy of Johannes De Groot and his namesake

## Photography[edit]

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.

### Mendocino County[edit]

Little River beach

Jug Handle Beach

Mendocino Beacon building

### Orange County[edit]

Bridge across North Lake, Woodbridge, Irvine, California

### Theoretical computer scientists[edit]

Knuth Prize presentation to Volker Strassen

Volker Strassen giving the Knuth Prize lecture

### Wall poems in Leiden[edit]

### Miscellaneous[edit]

"Balancing", by John Hooper