Abstract
AbstractThis paper proves that every (n + )‐chromatic graph contains a subgraph H with $\chi _c (H) = n$. This provides an easy method for constructing sparse graphs G with $\chi_c (G) = \chi ( G) = n$. It is also proved that for any ε > 0, for any fraction k/d > 2, there exists an integer g such that if G has girth at least g and $\chi _c (G) = k/d$ then for every vertex v of G, $\chi _c (G-{v})> k/d - \varepsilon $. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 95–105, 2003
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