Exklusive Graphen und Hamiltonche Graphenn-ten Grades II

The graphs considered are finite and undirected, loops do not occur. An induced subgraphI of a graphX is called animitation ofX, if

1. the degreesd _I(v)≡d _X(v) (mod 2) for allv∈V(I)
2. eachu∈V(X)?V(I) is connected with the setv(I) by an even number of edges. If the set of imitations ofX consists only ofX itself, thenX is anexclusive graph. AHamiltonian graph of degree n (abbr.:HG ⁿ) in the sense ofA. Kotzig is ann-regular graph (n>1) with a linear decomposition and with the property, that any two of the linear components together form a Hamiltonian circuit of the graph.

In the first chapter some theorems concerning exclusive graphs and Euler graphs are stated. Chapters 2 deals withHG ^n′ s and bipartite graphs. In chapters 3 a useful concept—theX-graph of anHG ⁿ—is defined; in this paper it is the conceptual connection between exclusive graphs andHG ^n′ s, since a graphG is anHG ⁿ, if all itsX-graphs are exlusive. Furthermore, some theorems onX-graphs are proved. Chapter 4 contains the quintessence of the paper: If we want to construct a newHG ⁿ F from anotherHG ⁿ G, we can consider certain properties of theX-graphs ofG to decide whetherF is also anHG ⁿ.