Erik E. Westlund

Learn More
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)
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)
Alspach conjectured that every connected Cayley graph of even valency on a finite Abelian group is Hamilton-decomposable. Using some techniques of Liu, this article shows that if A is an Abelian group of even order with a generating set {a, b}, and A contains a subgroup of index two, generated by c , then the 6-regular Cayley graph Cay(A; {a, b, c}) is(More)
Alspach conjectured that every connected Cayley graph on a finite Abelian group A is Hamiltondecomposable. Liu has shown that for |A| even, if S = {s1, . . . , sk} ⊂ 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 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)| 6∑σ∈C α(H(σ, L)) is satisfied, where C is(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, abbreviated (G,L), satisfies Hall’s condition if for each subgraph H of G, the inequality |V (H)| 6σ∈C α(H(σ, L)) is(More)
The following is a more detailed explanation of Section 2 of [3]: Let G be a finite abelian group, |G| = n and S = {s, t} where 〈s, t〉 = G, 0 / ∈ S, and s 6= ±t. If we assume that ord(s) ≥ ord(t) > 2, then the associated Cayley graph Γ = Cay(G, S) is simple, 4-regular, and connected. Clearly, if ord(s) = os and ord(t) = ot, then s and t generate 2-factors(More)
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 K2m+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(More)
  • 1