Scholarlink

<p>We obtain formulas for the maximum partial-dual genus of any orientable ribbon graph, and for the maximum partial-dual Euler-genus of any ribbon graph. This derivation involves the introduction of the <i>partial-dual deficiency</i> invariant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/10801_2026_1500_IEq1_HTML.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="120" Type="Linedraw" Width="44" /> </InlineMediaObject> </InlineEquation>, which is analogous to the Xuong deficiency <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\xi (G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ξ</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We also formulate a sufficient condition for a graph such that all ribbon graphs with that underlying graph have the same maximum partial-dual genus and the same maximum partial-dual Euler-genus.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The maximum partial-dual genus of a ribbon graph

  • 期刊论文

  • 发表日期：

    2026年1月30日

查看全文
  • Yichao Chen,
  • Jonathan L. Gross,
  • Thomas W. Tucker

摘要

We obtain formulas for the maximum partial-dual genus of any orientable ribbon graph, and for the maximum partial-dual Euler-genus of any ribbon graph. This derivation involves the introduction of the partial-dual deficiency invariant , which is analogous to the Xuong deficiency \(\xi (G)\) ξ ( G ) . We also formulate a sufficient condition for a graph such that all ribbon graphs with that underlying graph have the same maximum partial-dual genus and the same maximum partial-dual Euler-genus.