Graph homomorphism

Builds on Graph

Definition

Let $G$ and $H$ be graphs with vertex sets $V(G)$ and $V(H)$ . A graph homomorphism from $G$ to $H$ is a map $f : V(G) \to V(H)$ such that $f(u) \sim f(v)$ in $H$ whenever $u \sim v$ in $G$ .

Remarks

A homomorphism maps edges to edges. It may map non-adjacent vertices to adjacent ones, and it may map several vertices to one vertex. A homomorphism from $G$ to the complete graph $K_k$ is the same as a proper colouring of $G$ with $k$ colours. A bijective homomorphism whose inverse is also a homomorphism is a graph isomorphism.

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Graph definition
Graph homomorphism definition

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Hedetniemi's conjecture

Tag	`06SCB3R6BN`
URI	`m2://06SCB3R6BN`
Kind	definition
Writing	W1 stated
MSC	05C60
Defines	Graph homomorphism
Uses	Graph

Graph homomorphism

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

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