# Rainbow Tetrahedra in Cayley Graphs

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 4, page 733-754
- ISSN: 2083-5892

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topItalo J. Dejter. "Rainbow Tetrahedra in Cayley Graphs." Discussiones Mathematicae Graph Theory 35.4 (2015): 733-754. <http://eudml.org/doc/276027>.

@article{ItaloJ2015,

abstract = {Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)|1/3 and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly six connected subgraphs of the (3, 6, 3, 6)-semi- regular tessellation; and (c) 3 in exactly four connected subgraphs of the \{6, 3\}-regular hexagonal tessellation. These vertices have as closed neigh- borhoods the union (in a fixed way) of closed neighborhoods in the ten respective resulting tessellations.},

author = {Italo J. Dejter},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {rainbow triangles; rainbow tetrahedra; Cayley graphs},

language = {eng},

number = {4},

pages = {733-754},

title = {Rainbow Tetrahedra in Cayley Graphs},

url = {http://eudml.org/doc/276027},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Italo J. Dejter

TI - Rainbow Tetrahedra in Cayley Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 4

SP - 733

EP - 754

AB - Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)|1/3 and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly six connected subgraphs of the (3, 6, 3, 6)-semi- regular tessellation; and (c) 3 in exactly four connected subgraphs of the {6, 3}-regular hexagonal tessellation. These vertices have as closed neigh- borhoods the union (in a fixed way) of closed neighborhoods in the ten respective resulting tessellations.

LA - eng

KW - rainbow triangles; rainbow tetrahedra; Cayley graphs

UR - http://eudml.org/doc/276027

ER -

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