Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).

compiled April 30, 2009 from draft version hg:e0660c153c0b:79 An acyclic coloring of a graph is a proper vertex coloring such that the subgraph induced by the union of any two color classes is a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. The acyclic and star chromatic numbers ...

Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...

A (d,h)-decomposition of a graph G is an order pair (D,H) such that H subgraph where has the maximum degree at most h and D acyclic orientation G−E(H) out-degree d. (d,h)-decomposable if (d,h)-decomposition. Let be embeddable in surface nonnegative characteristic. It known (d,h)-decomposable, then h-defective d+1-choosable. In this paper, we investigate graphs prove following four results. (1) ...

1 Analyzing General Properties of Network Deconvolution 3 1.1 Network deconvolution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Optimality analysis of network deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Modeling assumptions and intuitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

A graph G is ramdomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H , can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize all ramdomly P3– decomposable graphs and ramdomly P4–decomposable graphs. We also characterize all ramdomly Pk–decomposable graphs of size 2k where all vertices have even ...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. Analogously, a tree is called T -decomposable for a fixed tree T if it has a spanning forest whose components are all isomorphic to T . In this paper, we use a generating functions approach to derive exact and asymptotic results on the number of k-decomposable and T -decomposable trees from a so-call...