Zero-free intervals of chromatic polynomials of hypergraphs

Abstract

In this paper, we prove that <math><mrow is="true"><mo is="true">(</mo><mo linebreak="goodbreak" linebreakstyle="after" is="true">−</mo><mi is="true">∞</mi><mo is="true">,</mo><mn is="true">0</mn><mo is="true">)</mo></mrow></math> is a zero-free interval for chromatic polynomials of a family <math><msub is="true"><mrow is="true"><mi mathvariant="script" is="true">L</mi></mrow><mrow is="true"><mn is="true">0</mn></mrow></msub></math> of hypergraphs and <math><mrow is="true"><mo is="true">(</mo><mn is="true">0</mn><mo is="true">,</mo><mn is="true">1</mn><mo is="true">)</mo></mrow></math> is a zero-free interval for chromatic polynomials of a subfamily <math><msubsup is="true"><mrow is="true"><mi mathvariant="script" is="true">L</mi></mrow><mrow is="true"><mn is="true">0</mn></mrow><mrow is="true"><mo is="true">′</mo></mrow></msubsup></math> of <math><msub is="true"><mrow is="true"><mi mathvariant="script" is="true">L</mi></mrow><mrow is="true"><mn is="true">0</mn></mrow></msub></math> of hypergraphs. These results extend known results on zero-free intervals of chromatic polynomials of graphs and hypergraphs.