# Odd-angulated graphs and cancelling factors in box products

Zhongyuan Che, Karen L. Collins, Claude Tardif

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

Under what conditions is it true that if there is a graph homomorphism G H → G T, then there is a graph homomorphism H → T? Let G be a connected graph of odd girth 2k + 1. We say that G is (2 k + 1 )-angulated if every two vertices of G are joined by a path each of whose edges lies on some (2k + 1)-cycle. We call G strongly (2k + 1)-angulated if every two vertices are connected by a sequence of (2k + 1)-cycles with consecutive cycles sharing at least one edge. We prove that if G is strongly (2k + 1)-angulated, H is any graph, S, T are graphs with odd girth at least 2k+ 1, and φ: G H → S T is a graph homomorphism, then either φ maps G {h} to S {th} for all h ∈ V(H) where th ∈ V(T) depends on h; or φ maps G {h} to {sh} T for all h ∈ V(H) where sh ∈ V(S) depends on h. This theorem allows us to prove several sufficient conditions for a cancelation law of a graph homomorphism between two box products with a common factor. We conclude the article with some open questions.

Original language English (US) 221-238 18 Journal of Graph Theory 58 3 https://doi.org/10.1002/jgt.20307 Published - Jul 1 2008

### Fingerprint

Box Product
Graph Homomorphism
Odd
Girth
Graph in graph theory
Cycle
Common factor
Cancellation
Connected graph
Consecutive
Sharing
Path
Sufficient Conditions
Theorem

### All Science Journal Classification (ASJC) codes

• Geometry and Topology

### Cite this

Che, Zhongyuan ; Collins, Karen L. ; Tardif, Claude. / Odd-angulated graphs and cancelling factors in box products. In: Journal of Graph Theory. 2008 ; Vol. 58, No. 3. pp. 221-238.
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Odd-angulated graphs and cancelling factors in box products. / Che, Zhongyuan; Collins, Karen L.; Tardif, Claude.

In: Journal of Graph Theory, Vol. 58, No. 3, 01.07.2008, p. 221-238.

Research output: Contribution to journalArticle

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