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It was shown in a recent paper that an rs‐ regular multigraph G with maximum multiplicity μ(G) ≤ r can be factored into r regular simple graphs if first we allow the deletion of a relatively small ...
, respectively. If AC_E(c)(A@(G)), then G U A ( G - A ) denotes the graph obtained from G if we add ( delete ) the edges in A to ( from ) G. The degree of vertex x in G is written d c ( x ) ,and G [ Z ] denotes ...
A graph is (r,k)- factor -critical if the removal of any set of k vertices results in a graph with an r- factor (i.e. with an r- regular spanning subgraph ). We show that every τ-tough graph of order n ...
and contrasting areas, namely regular graphs and treelike graphs . We think of a graph as treelike if by deleting a few edges we may obtain a graph with low treewidth (treewidth measures how much we have to ‘fatten ...
gives a spanning, |$r$|- regular subgraph of |$G$|. We refer to such a subgraph as an |$r$|- factor of |$G$|. Given an oriented graph |$G$|, let |${\text{reg}}(G)$| be the maximal integer |$r$| for which ...
such that $$D \geq n/4$$. Then $$G$$ contains a Hamilton cycle. The $$3$$- regular graph obtained from the Petersen graph by replacing one vertex with a triangle shows that the conjecture does not hold for $$n=12 ...
behavior of the entry distribution of eigenvectors of random regular graphs by studying factors of i.i.d. processes on the regular infinite tree. In all of these works the randomness of the model is used ...
. The Petersen graph is strongly regular : (a) it is regular , meaning that each vertex has the same number of adjacent vertices (neighbours, in this case three), (b) every pair of adjacent vertices has the same ...
— from the source |$u$| to the target |$v$|—whereas an undirected edge represents a bidirectional connection. An edge is reflexive if its source and target are the same vertex . A simple graph may contain ...
a result from [19] falls short by a factor of |$O(\sqrt{\log n})$|. Another advantage over vertex expansion is that, often, edge expansion is easier to verify. Let |$G = (V, E)$| be a graph with |$n ...
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