Embedding Partial <i>k</i>‐Star Designs

Hoffman, D. G.; Roberts, Dan

doi:10.1002/jcd.21353

Cited by 3 publications

(4 citation statements)

References 4 publications

(4 reference statements)

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“…In opposite situations, in concentrated environments with predictable demand, IT can be associated with increased vertical integration, thanks to firms using IT to coordinate activities within the firm in order to increase revenue and capture added value. Similarly, these observations contribute to explanations of the different behaviors of B2B (businessto-business) exchanges, which are also influenced by industry environments [28]: when demand uncertainty is high, firms are more likely to adopt B2B electronic exchanges and coordinate with suppliers and customers; this idea is shared by Hoffman [30]. On the other hand, in more concentrated environments, such as in the chemical industry, B2B exchanges are used to coordinate activities with business partners with whom there are ongoing relationships [31].…”

Section: Analysis and Exploration Of Key Concepts And Cluster Structuresmentioning

confidence: 94%

Vertical Integration Dynamics to Innovate in Technology Business

et al. 2023

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Companies try to acquire the finest advantages and techniques in a technologically advanced and end-to-end market to have a stronger foothold there. Although empirical research on this topic links IT to a decline in vertical integration, corporations are increasingly using this corporate strategy. The goal of this study is to show how over the past 22 years, scientific literature has changed with regard to how information technology (IT) affects vertical integration, one of the main types of corporate strategies. The findings demonstrated that vertical integration has been evolving in a balanced manner in a technological environment. Three categories—information technology, innovation, and processes—help explain this association and were discovered through cluster analysis. The direction of operational integration, the degree of industry concentration, demand unpredictability, and innovation should all be considered while making integration decisions.

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Section: Analysis and Exploration Of Key Concepts And Cluster Structuresmentioning

confidence: 94%

Vertical Integration Dynamics to Innovate in Technology Business

et al. 2023

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“…Using s " 3k − n + 1, (17) is at least k(4n − 7k − 4 √ 2n − 2k − 1). In turn this can be shown to be positive using n >7 4 k 6k + 6 + 5 4 .…”

mentioning

confidence: 95%

“…So by Lemma 14 there is a k-star decomposition of L ∨ K s . Suppose that k + 1 " n "7 4 k. We show that we can embed D in a k-star decomposition of K 3k . Let s = 3k − n and note that k " s <9 4 k since k + 1 " n "7 4 k and that !…”

mentioning

confidence: 99%

“…This paper is concerned with the problem of when a partial k-star decomposition of K n can be embedded in a k-star decomposition of K n+s . In 2012, Hoffman and Roberts [7] proved that a partial k-star decomposition of K n can be embedded in a k-star decomposition of K n+s for some positive integer s such that s " 7k − 4 when k is odd and s " 8k − 4 when k is even. Furthermore, they conjectured that the smallest possible upper bound on s is around 2k.…”

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confidence: 99%

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Smaller Embeddings of Partial $k$-Star Decompositions

Gunasekara

Horsley

2023

Electron. J. Combin.

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A $k$-star is a complete bipartite graph $K_{1,k}$. For a graph $G$, a $k$-star decomposition of $G$ is a set of $k$-stars in $G$ whose edge sets partition the edge set of $G$. If we weaken this condition to only demand that each edge of $G$ is in at most one $k$-star, then the resulting object is a partial $k$-star decomposition of $G$. An embedding of a partial $k$-star decomposition $\mathcal{A}$ of a graph $G$ is a partial $k$-star decomposition $\mathcal{B}$ of another graph $H$ such that $\mathcal{A} \subseteq \mathcal{B}$ and $G$ is a subgraph of $H$. This paper considers the problem of when a partial $k$-star decomposition of $K_n$ can be embedded in a $k$-star decomposition of $K_{n+s}$ for a given integer $s$. We improve a result of Noble and Richardson, itself an improvement of a result of Hoffman and Roberts, by showing that any partial $k$-star decomposition of $K_n$ can be embedded in a $k$-star decomposition of $K_{n+s}$ for some $s$ such that $s < \frac{9}{4}k$ when $k$ is odd and $s < (6-2\sqrt{2})k$ when $k$ is even. For general $k$, these constants cannot be improved. We also obtain stronger results subject to placing a lower bound on $n$.

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Balls, bins, and embeddings of partial k-star designs

Noble

Richardson

2019

Discrete Mathematics

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Embedding Partial k‐Star Designs

Cited by 3 publications

References 4 publications

Vertical Integration Dynamics to Innovate in Technology Business

Vertical Integration Dynamics to Innovate in Technology Business

Smaller Embeddings of Partial $k$-Star Decompositions

Balls, bins, and embeddings of partial k-star designs

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