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<p>We consider a graph theory problem motivated by the self-assembly of DNA graph structures using branched junction molecules with flexible arms (called ‘tiles’ in the combinatorial model). More precisely, we want to determine a set of tiles that realizes a target graph <i>G</i> using the minimum number of bond-edge types so that no graph with order smaller than <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\vert V(G)\vert\)</EquationSource> </InlineEquation> can be realized; the parameter of interest is denoted by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(B_2(G)\)</EquationSource> </InlineEquation>. We present an approach that provides an upper bound for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(B_2(G)\)</EquationSource> </InlineEquation> using certain multipartite subgraphs of <i>G</i>. We provide some numerical conditions characterizing such multipartite graphs in terms of the degree of their vertices. Then, we apply our method to the graphs corresponding to the Platonic solids.</p>

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A multipartite approach for the self-assembly of DNA graph structures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月4日

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  • S. Bonvicini,
  • M. M. Ferrari

摘要

We consider a graph theory problem motivated by the self-assembly of DNA graph structures using branched junction molecules with flexible arms (called ‘tiles’ in the combinatorial model). More precisely, we want to determine a set of tiles that realizes a target graph G using the minimum number of bond-edge types so that no graph with order smaller than \(\vert V(G)\vert\) can be realized; the parameter of interest is denoted by \(B_2(G)\) . We present an approach that provides an upper bound for \(B_2(G)\) using certain multipartite subgraphs of G. We provide some numerical conditions characterizing such multipartite graphs in terms of the degree of their vertices. Then, we apply our method to the graphs corresponding to the Platonic solids.