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- Antonio J Golubski, Erik E Westlund, John Vandermeer, Mercedes Pascual
- Trends in ecology & evolution
- 2016

Analyses of ecological network structure have yielded important insights into the functioning of complex ecological systems. However, such analyses almost universally omit non-pairwise interactions, many classes of which are crucial for system structure, function, and resilience. Hypergraphs are mathematical constructs capable of considering such… (More)

- Erik E. Westlund, Jiuqiang Liu, Donald L. Kreher
- Discrete Mathematics
- 2009

- ERIK E. WESTLUND
- 2014

Z2 ⊕ Z12 {(1, 4), (1, 5), (0, 3)}, {(1, 3), (1, 4), (0, 3)}, {(0, 1), (0, 2), (1, 1)}, {(1, 3), (0, 4), (1, 2)}, {(1, 3), (1, 5), (0, 3)}, {(0, 4), (0, 5), (1, 2)}, {(0, 2), (1, 5), (1, 2)}, {(1, 3), (0, 1), (1, 5)}, {(0, 1), (0, 3), (1, 2)}, {(1, 3), (0, 1), (0, 4)}, {(0, 2), (0, 3), (1, 2)}, {(1, 4), (1, 1), (1, 2)}, {(1, 4), (1, 5), (0, 5)}, {(1, 3), (0,… (More)

- Erik E. Westlund
- Discrete Mathematics
- 2014

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)

- Erik E. Westlund
- Discrete Mathematics
- 2012

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)

- Sarah Holliday, Jennifer Vandenbussche, Erik E. Westlund
- Electr. J. Comb.
- 2015

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)

- Sarah Holliday, Jennifer Vandenbussche, Erik E. Westlund
- Electr. J. Comb.
- 2016

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)

- Mari F. Castle, Evan D. Moore, Erik E. Westlund
- Australasian J. Combinatorics
- 2015

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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