Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

• Autorzy: Izak Broere , Jozef Bucko , Peter Mihók
• Języki publikacji: EN

Abstrakty

EN

Let 𝓟₁,𝓟₂,...,𝓟ₙ be graph properties, a graph G is said to be uniquely (𝓟₁,𝓟₂, ...,𝓟ₙ)-partitionable if there is exactly one (unordered) partition {V₁,V₂,...,Vₙ} of V(G) such that $G[V_i] ∈ 𝓟_i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (𝓟₁,𝓟₂,...,𝓟ₙ)-partitionable graphs exist if and only if $𝓟_i$ and $𝓟_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ {1,2,...,n}.

Słowa kluczowe

EN

induced-hereditary properties; reducibility; divisibility; uniquely partitionable graphs.

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 31-37

Daty

wydano

2002

otrzymano

2000-08-08

poprawiono

2001-07-02

Twórcy

autor

Izak Broere

• Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa

autor

Jozef Bucko

• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic

autor

Peter Mihók

• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
• Mathematical Institute, Slovak Academy of Science, Gresákova 6, 040 01 Košice, Slovak Republic

Bibliografia

• [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, Survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [3] I. Broere and J. Bucko, Divisibility in additive hereditary graph properties and uniquely partitionable graphs, Tatra Mt. Math. Publ. 18 (1999) 79-87.
• [4] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043.
• [5] F. Harary, S.T. Hedetniemi and R.W. Robinson, Uniquely colourable graphs, J. Combin. Theory 6 (1969) 264-270, doi: 10.1016/S0021-9800(69)80086-4.
• [6] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58.
• [7] P. Mihók, Unique factorization theorem, Discuss. Math. Graph Theory 20 (2000) 143-154, doi: 10.7151/dmgt.1114.

Identyfikatory

DOI

10.7151/dmgt.1156