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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 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)
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)
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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