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A note on minimal directed graphs with given girth

✍ Scribed by Yahya Ould Hamidoune


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
306 KB
Volume
43
Category
Article
ISSN
0095-8956

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The oriented chromatic number o(H) of an oriented graph H is defined to be the minimum order of an oriented graph H' such that H has a homomorphism to H'. If each graph in a class ~ has a homomorphism to the same H', then H' is ~-universal. Let ~k denote the class of orientations of planar graphs wi

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## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and KovΓ‘cs [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209–218]. A (Ξ΄, __g__)‐cage is a small