Category:Subdivisions (Graph Theory)
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This category contains results about subdivisions in the context of Graph Theory.
Definitions specific to this category can be found in Definitions/Subdivisions (Graph Theory).
Let $G = \struct {V, E}$ be a graph.
Edge Subdivision
The edge subdivision operation for an edge $\set {u, v} \in E$ is the deletion of $\set {u, v}$ from $G$ and the addition of two edges $\set {u, w}$ and $\set {w, v}$ along with the new vertex $w$.
This operation generates a new graph $H$:
- $H = \struct {V \cup \set w, \paren {E \setminus \set {u, v} } \cup \set {\set {u, w}, \set {w, v} } }$
Graph Subdivision
A graph which has been derived from $G$ by a sequence of edge subdivision operations is called a subdivision of $G$.
Subcategories
This category has only the following subcategory.