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## Discussiones Mathematicae Graph Theory

1998 | 18 | 2 | 233-242
Tytuł artykułu

### 2-halvable complete 4-partite graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A complete 4-partite graph $K_{m₁,m₂,m₃,m₄}$ is called d-halvable if it can be decomposed into two isomorphic factors of diameter d. In the class of graphs $K_{m₁,m₂,m₃,m₄}$ with at most one odd part all d-halvable graphs are known. In the class of biregular graphs $K_{m₁,m₂,m₃,m₄}$ with four odd parts (i.e., the graphs $K_{m,m,m,n}$ and $K_{m,m,n,n}$) all d-halvable graphs are known as well, except for the graphs $K_{m,m,n,n}$ when d = 2 and n ≠ m. We prove that such graphs are 2-halvable iff n,m ≥ 3. We also determine a new class of non-halvable graphs $K_{m₁,m₂,m₃,m₄}$ with three or four different odd parts.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
233-242
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-03-09
poprawiono
1998-08-03
Twórcy
autor
• Department of Applied Mathematics, Technical University Ostrava, 17 listopadu, 708 33 Ostrava, Czech Republic
Bibliografia
• [1] M. Behzad, G. Chartrand and L. Lesniak-Foster, Graphs and Digraphs (Prindle, Weber & Schmidt, Boston, 1979).
• [2] J. Bosák, A. Rosa and Š. Znám, On decompositions of complete graphs into factors with given diameters, in: Theory of Graphs, Proc. Coll. Tihany 1966 (Akadémiai Kiadó, Budapest, 1968) 37-56.
• [3] D. Fronček, Decompositions of complete bipartite and tripartite graphs into selfcomplementary factors with finite diameters, Graphs. Combin. 12 (1996) 305-320, doi: 10.1007/BF01858463.
• [4] D. Fronček, Decompositions of complete multipartite graphs into selfcomplementary factors with finite diameters, Australas. J. Combin. 13 (1996) 61-74.
• [5] D. Fronček, Decompositions of complete multipartite graphs into disconnected selfcomplementary factors, Utilitas Mathematica 53 (1998) 201-216.
• [6] D. Fronček and J. Širáň, Halving complete 4-partite graphs, Ars Combinatoria (to appear).
• [7] T. Gangopadhyay, Range of diameters in a graph and its r-partite complement, Ars Combinatoria 18 (1983) 61-80.
• [8] P. Híc and D. Palumbíny, Isomorphic factorizations of complete graphs into factors with a given diameter, Math. Slovaca 37 (1987) 247-254.
• [9] A. Kotzig and A. Rosa, Decomposition of complete graphs into isomorphic factors with a given diameter, Bull. London Math. Soc. 7 (1975) 51-57, doi: 10.1112/blms/7.1.51.
• [10] D. Palumbíny, Factorizations of complete graphs into isomorphic factors with a given diameter, Zborník Pedagogickej Fakulty v Nitre, Matematika 2 (1982) 21-32.
• [11] P. Tomasta, Decompositions of graphs and hypergraphs into isomorphic factors with a given diameter, Czechoslovak Math. J. 27 (1977) 598-608.
• [12] E. Tomová, Decomposition of complete bipartite graphs into factors with given diameters, Math. Slovaca 27 (1977) 113-128.
Typ dokumentu
Bibliografia
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