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{{Short description|Graph whose embedding in a Euclidean space forms a regular tiling}} [[File:Square grid graph.svg|thumb|[[Square tiling|Square grid]] graph]] ...

{{distinguish|text = the [[Heawood graph]], which is a member of the Heawood graph family}} ...erm '''Heawood family''' refers to either one of the following two related graph families generated via [[ΔY- and YΔ-transformations]]: ...

{{Short description|Graph width parameter used in graph theory}} '''Rank-width''' is a graph width parameter used in [[graph theory]] and [[parameterized complexity]], and defined using [[linear algebra]]. ...

...l" because a [[perfect matching]] is able to be created with the remaining graph (cycle 3 leaves no vertices, automatically filling this criteria). Right: A Pfaffian Orientation of the graph on the left, where the edges of the 3 cycles from the right have an odd num ...

{{Short description|Cubic graph with 8 vertices and 12 edges}} {{infobox graph ...

{{short description|Graph coloring in which every 4-vertex path uses ≥3 colors}} ...ph star coloring.svg|thumb|right|300px|The star chromatic number of [[Dyck graph]] is 4, while the chromatic number is 2.]] ...

...act. The amalgamation can then be used to study properties of the original graph in an easier to understand context. Applications include embeddings,<ref na Note that while <math>G</math> can be a graph or a [[pseudograph]], it will usually be the case that <math>H</math> is a ...

...D.svg|300px|right|Depiction of the ΔY- and YΔ-transformations applied to a graph]] ...(discrete mathematics)|graphs]]. A ΔY-transformation replaces a [[triangle graph|triangle]] by a vertex of [[vertex degree|degree]] three; and conversely, a ...

...extending the mathematical results and building new algorithmic tools. The theory was introduced in the work of [[Erik Demaine|Demaine]], [[Fedor_Fomin|Fom A parameterized problem <math>\Pi</math> is ''minor-bidimensional'' if ...

....svg|thumb|{{math|''K''₅}} subdivision of the 12-vertex [[crown graph]]]] ...a [[Homeomorphism (graph theory)|subdivision]] of the 5-vertex [[complete graph]] {{math|''K''₅}}. It is named for [[Paul Seymour (mathematician ...

{{unsolved|mathematics|Do minor-closed graph families have <math>\ell_1</math> embeddings with bounded distortion?}} ...etric geometry]], the '''GNRS conjecture''' connects the theory of [[graph minor]]s, the [[stretch factor]] of [[embedding]]s, and the [[approximation ratio ...

In [[Matroid|matroid theory]], a '''binary matroid''' is a matroid that can be [[Matroid representation | title = Matroid Theory ...

{{DISPLAYTITLE:''k''-outerplanar graph}} ...tices on the third layer (darker yellow). Because of the symmetries of the graph, no other embedding has fewer layers.]] ...

| title = Matroid Theory | title = Matroid Theory ...

...[[polynomial-time approximation scheme]]s (PTASs) for problems on [[planar graph]]s. It is named after [[Brenda Baker]], who announced it in a 1983 conferen The idea for Baker's technique is to break the graph into layers, such that the problem can be solved optimally on each layer, t ...

{{Short description|Min-max theorem in graph theory}} ...and [[Lajos Pósa (mathematician)|Lajos Pósa]], relates two parameters of a graph: ...

...ht graph.dot.svg|thumb|The [[Frucht graph]], a 3-[[regular graph|regular]] graph whose automorphism group realizes the [[trivial group]].]] ...y [[graph isomorphism|non-isomorphic]] [[simple graph|simple]] [[connected graph|connected]] graphs such that the [[automorphism group]] of each of them is ...

...e reached by vertex-disjoint [[Path (graph theory)|paths]] in a [[directed graph]]. | title = Applications of Menger's graph theorem ...

...ns of matroid families by forbidden minors, analogous to the corresponding theory in graphs. A matroid ''N'' is a minor of a matroid ''M'' if it can be constructed from ''M'' by restriction and c ...

In [[matroid theory]], an '''Eulerian matroid''' is a matroid whose elements can be partitioned ...o not contain any line. The three-point circuits are the [[complement (set theory)|complements]] of the four-point circuits, so it is possible to partition t ...