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Alspach conjectured that every connected Cayley graph on a finite Abelian group A is Hamilton-decomposable. Liu has shown that for |A| even, if S = {s 1 ,. .. , s k } ⊂ A is an inverse-free strongly minimal generating set of A, then the Cayley graph Cay(A; S), is decomposable into k Hamilton cycles, where S denotes the inverse-closure of S. Extending these… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Alspach conjectured that every connected Cayley graph of even valency… (More)

In the context of list-coloring the vertices of a graph, Hall's condition is a generalization of Hall's Marriage Theorem and is necessary (but not sufficient) for a graph to admit a proper list-coloring. The graph G with list assignment L satisfies Hall's condition if for each subgraph H of G, the inequality |V (H)| σ∈C α(H(σ, L)) is satisfied, where C is… (More)

- Laura Owen, Erik Westlund, Andy Gutierrez, Vivian Lee
- 2015

Closing postsecondary opportunity gaps has become a naonal, state and local educaonal priority. To help eliminate these gaps, the U.S. Department of Educaon iniated a project that provided real‐‐me, student‐level Free Applicaon for Federal Student Aid (FAFSA) compleon status to large, urban school districts. Leveraging this informaon, school counselors… (More)

We investigate the problem of decomposing the edges of a connected circulant graph with n vertices and generating set S into isomorphic subgraphs each having n edges. For 8-regular circulants, we show this is always possible when s + 2 ≤ n/4 for all edge lengths s ∈ S.

In the context of list coloring the vertices of a graph, Hall's condition is a generalization of Hall's Marriage Theorem and is necessary (but not sufficient) for a graph to admit a proper list coloring. The graph G with list assignment L, abbreviated (G, L), satisfies Hall's condition if for each subgraph H of G, the inequality |V (H)| σ∈C α(H(σ, L)) is… (More)

- Erik E. Westlund
- 2015

Date To my family.

For a tree T , the graph X is T-decomposable if there exists a partition of the edge set of X into isomorphic copies of T. In 1963, Ringel conjectured that K 2m+1 can be decomposed by any tree with m edges. Graham and Häggkvist conjectured more generally that every 2m-regular graph can be decomposed by any tree with m edges. Fink showed in 1994 that for any… (More)

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