Displaying similar documents to “О регулярных графах Тервиллигера с μ = 2 ”

2-halvable complete 4-partite graphs

Dalibor Fronček (1998)

Discussiones Mathematicae Graph Theory

Similarity:

A complete 4-partite graph K m ₁ , m ₂ , m ₃ , m ₄ is called d-halvable if it can be decomposed into two isomorphic factors of diameter d. In the class of graphs K m ₁ , m ₂ , m ₃ , m ₄ with at most one odd part all d-halvable graphs are known. In the class of biregular graphs K m ₁ , m ₂ , m ₃ , m ₄ 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 m ₁ , m ₂ , m ₃ , m ₄ with three...

The order of uniquely partitionable graphs

Izak Broere, Marietjie Frick, Peter Mihók (1997)

Discussiones Mathematicae Graph Theory

Similarity:

Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition V₁,...,Vₙ of V(G) such that, for each i = 1,...,n, the subgraph of G induced by V i has property i . If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.