Edge-deletion and edge-contraction problems

1982 ◽  
Author(s):  
Takao Asano ◽  
Tomio Hirata
Keyword(s):  
Edge Deletion ◽  
Edge Contraction

scholarly journals Posets from Admissible Coxeter Sequences

10.37236/684 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Matthew Macauley ◽  
Henning S. Mortveit
Keyword(s):  
Coxeter Groups ◽  
Conjugacy Problem ◽  
Equivalence Classes ◽  
Quiver Representations ◽  
Edge Deletion ◽  
Acyclic Orientations ◽  
Edge Contraction ◽  
Combinatorial Invariant ◽  
Source To Sink ◽  
Admissible Sequences

We study the equivalence relation on the set of acyclic orientations of an undirected graph $\Gamma$ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in turn, the admissible sequences. This allows us to construct an explicit bijection from the equivalence classes over $\Gamma$ to those over $\Gamma'$ and $\Gamma"$, the graphs obtained from $\Gamma$ by edge deletion and edge contraction of a fixed cycle-edge, respectively. This bijection yields quick and elegant proofs of two non-trivial results: $(i)$ A complete combinatorial invariant of the equivalence classes, and $(ii)$ a solution to the conjugacy problem of Coxeter elements for simply-laced Coxeter groups. The latter was recently proven by H. Eriksson and K. Eriksson using a much different approach.

scholarly journals A Bijection for Tricellular Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hillary S. W. Han ◽  
Christian M. Reidys
Keyword(s):  
Matrix Theory ◽  
Dyson Equation ◽  
Cutting Edge ◽  
Edge Deletion ◽  
Cell Complexes ◽  
Bijective Proof ◽  
Edge Contraction ◽  
Orientable Surfaces

We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory (Dyson, 1949) employing the Schwinger-Dyson equation (Schwinger, 1951). In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus g into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge cutting, edge contraction, and edge deletion.

scholarly journals On the removal of forbidden graphs by edge-deletion or by edge-contraction

1981 ◽  
Vol 3 (2) ◽  
pp. 151-153 ◽  
Author(s):  
Toshimasa Watanabe ◽  
Tadashi Ae ◽  
Akira Nakamura
Keyword(s):  
Edge Deletion ◽  
Edge Contraction

In vitro and in vivo Effect of Platelet-Rich Plasma-Based Autologous Topical Serum on Cutaneous Wound Healing

2021 ◽  
pp. 1-13
Author(s):  
Eduardo Anitua ◽  
Victoria Muñoz ◽  
Libe Aspe ◽  
Roberto Tierno ◽  
Adrian García-Salvador ◽  
...  
Keyword(s):  
Wound Healing ◽  
Tissue Damage ◽  
Collagen Synthesis ◽  
Dermal Fibroblast ◽  
Platelet Rich Plasma ◽  
Cell Activity ◽  
Cutaneous Wound Healing ◽  
Cutaneous Wound ◽  
Fibroblast Migration ◽  
Edge Contraction

<b><i>Introduction:</i></b> Skin injury and wound healing is an inevitable event during lifetime. However, several complications may hamper the regeneration of the cutaneous tissue and lead to a chronic profile that prolongs patient recovery. Platelet-rich plasma is rising as an effective and safe alternative to the management of wounds. However, this technology presents some limitations such as the need for repeated blood extractions and health-care interventions. <b><i>Objective:</i></b> The aim of this study was to assess the use of an endogenous and storable topical serum (ES) derived from plasma rich in growth factors promoting wound healing, and to obtain preliminary data regarding its clinical and experimental effect over ulcerated skin models and patient care. <b><i>Methods:</i></b> Human dermal fibroblast and 3D organotypic ulcerated skin models were used to assess ES over the main mechanisms of wound healing including cell migration, edge contraction, collagen synthesis, tissue damage, extracellular matrix remodeling, cell death, metabolic activity, and histomorphometry analysis. Additionally, 4 patients suffering from skin wounds were treated and clinically assessed. <b><i>Results:</i></b> ES promoted dermal fibroblast migration, wound edge contraction, and collagen synthesis. When topically applied, ES increased collagen and elastin deposition and reduced tissue damage. The interstitial edema, structural integrity, and cell activity were also maintained, and apoptotic levels were reduced. Patients suffering from hard-to-heal wounds of different etiologies were treated with ES, and the ulcers healed completely within few weeks with no reported adverse events. <b><i>Conclusion:</i></b> This preliminary study suggests that ES might promote cutaneous wound healing and may be useful for accelerating the re-epithelization of skin ulcers.

An improved branching algorithm for the proper interval edge deletion problem

2021 ◽  
Vol 16 (2) ◽  
Author(s):  
Wenjun Li ◽  
Xiaojing Tang ◽  
Yongjie Yang
Keyword(s):  
Edge Deletion

scholarly journals Triangle edge deletion on planar glasses-free RGB-digraphs

2019 ◽  
Vol 788 ◽  
pp. 2-11 ◽  
Author(s):  
Dongjing Miao ◽  
Zhipeng Cai ◽  
Jiguo Yu ◽  
Yingshu Li
Keyword(s):  
Edge Deletion
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