Editing Glossary of graph theory (section)

==F==
{{glossary}}

{{term|face}}
{{defn|In a [[planar graph|plane graph]] or [[graph embedding]], a connected component of the subset of the plane or surface of the embedding that is disjoint from the graph. For an embedding in the plane, all but one face will be bounded; the one exceptional face that extends to infinity is called the outer (or infinite) face.}}

{{term|factor}}
{{defn|A factor of a graph is a spanning subgraph: a subgraph that includes all of the vertices of the graph. The term is primarily used in the context of regular subgraphs: a {{mvar|k}}-factor is a factor that is {{mvar|k}}-regular. In particular, a {{math|1}}-factor is the same thing as a perfect matching. A [[factor-critical graph]] is a graph for which deleting any one vertex produces a graph with a {{math|1}}-factor.}}

{{term|factorization}}
{{defn|A [[graph factorization]] is a partition of the edges of the graph into factors; a {{mvar|k}}-factorization is a partition into {{mvar|k}}-factors. For instance a {{math|1}}-factorization is an edge coloring with the additional property that each vertex is incident to an edge of each color.}}

{{term|family}}
{{defn|A synonym for {{gli|class}}.}}

{{term|finite}}
{{defn|A graph is finite if it has a finite number of vertices and a finite number of edges. Many sources assume that all graphs are finite without explicitly saying so. A graph is locally finite if each vertex has a finite number of incident edges. An infinite graph is a graph that is not finite: it has infinitely many vertices, infinitely many edges, or both.}}

{{term|first order}}
{{defn|The first order [[logic of graphs]] is a form of logic in which variables represent vertices of a graph, and there exists a binary predicate to test whether two vertices are adjacent. To be distinguished from second order logic, in which variables can also represent sets of vertices or edges.}}

{{term|-flap}}
{{defn|For a set of vertices {{mvar|X}}, an {{mvar|X}}-flap is a connected component of the induced subgraph formed by deleting {{mvar|X}}. The flap terminology is commonly used in the context of ''havens'', functions that map small sets of vertices to their flaps. See also the {{gli|bridge}} of a cycle, which is either a flap of the cycle vertices or a chord of the cycle.}}

{{term|forbidden}}
{{defn|A [[forbidden graph characterization]] is a characterization of a family of graphs as being the graphs that do not have certain other graphs as subgraphs, induced subgraphs, or minors. If {{mvar|H}} is one of the graphs that does not occur as a subgraph, induced subgraph, or minor, then {{mvar|H}} is said to be forbidden.}}

{{term|forcing graph}}
{{defn|A [[forcing graph]] is a graph {{mvar|H}} such that evaluating the subgraph density of {{mvar|H}} in the graphs of a graph sequence {{mvar|G(n)}} is sufficient to test whether that sequence is {{gli|quasi-random graph sequence|quasi-random}}.}}

{{term|forest}}
{{defn|A [[Tree (graph theory)|forest]] is an undirected graph without cycles (a disjoint union of unrooted trees), or a directed graph formed as a disjoint union of rooted trees.}}

{{term|free edge}}
{{defn|An [[Edge (graph theory)|edge]] which is not in a [[matching (graph theory)|matching]].}}

{{term|free vertex}}
{{defn|no=1|A [[Vertex (graph theory)|vertex]] not on a matched [[Edge (graph theory)|edge]] in a [[matching (graph theory)|matching]]}}
{{defn|no=2|A vertex which has not been matched.}}

{{term|Frucht}}
{{defn|no=1|[[Robert Frucht]]}}
{{defn|no=2|The [[Frucht graph]], one of the two smallest cubic graphs with no nontrivial symmetries.}}
{{defn|no=3|[[Frucht's theorem]] that every finite group is the group of symmetries of a finite graph.}}

{{term|full}}
{{defn|Synonym for {{gli|induced}}.}}

{{term|functional graph}}
{{defn|A [[functional graph]] is a directed graph where every vertex has out-degree one.  Equivalently, a functional graph is a maximal directed pseudoforest.}}

{{glossary end}}