# regular graph

(redirected from*K-regular graph*)

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We say that a k-regular graph G admits a Hamilton cycle decomposition, if the edge set of G can be partitioned into Hamilton cycles or Hamilton cycles together with a 1-factor according as k is even or odd, respectively.

In addition, the complete graph [9, 13], k nearest neighboring graph or k-regular graph [13, 15], or the close-loop graph [14] is applied to simulate the local graph structure in different saliency models.

Theorem:The k-regular graph (graph where all vertices have degree k) is a knight subgraph only for k [less than or equal to] 4.

For any k-regular graph G, k [greater than or equal to] 3, [gamma](G) = q - p.

For equal bipartition k-regular graph, the following corollary holds.

We determine the fixed-parameter complexity of several closely related variants: we prove that switching to a graph of maximum degree at most k is fixed parameter tractable, as well as of switching to a graph of minimum degree at least k, and of switching to a k-regular graph.

k+3])-time algorithm for deciding if a given graph can be switched to a graph with all vertex degrees at most k, or to a k-regular graph.

In an arbitrary k-regular graph, each vertex has degree at most k, which means that we can use our previous algorithm from Subsection 3.

A cage is a k-regular graph with girth g having the smallest possible number of vertices.

As defined by Biggs [7], the excess of a k-regular graph G is the difference jV (G)j-n0(k; g).

As already mentioned in the Introduction, our main aim is to obtain incidence matrices of bipartite k-regular graphs of girth 8 with small excess.

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