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Minimal reducible bounds for hom-properties of graphs

100%

Berger A., Broere I.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 2

143-158

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

A note on uniquely H-colourable graphs

100%

Bonato A.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

39-44

For a graph H, we compare two notions of uniquely H-colourable graphs, where one is defined via automorphisms, the second by vertex partitions. We prove that the two notions of uniquely H-colourable are not identical for all H, and we give a condition for when they are identical. The condition is related to the first homomorphism theorem from algebra.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Berger A.

1 Bonato A.

1 Broere I.

1 2007

1 1999

Wyniki wyszukiwania

Minimal reducible bounds for hom-properties of graphs

A note on uniquely H-colourable graphs