A note on fractional covers of a graph

A fractional colouring of a graph G is function that assigns non-negative real value to all possible colour-classes containing any vertex G, such the sum these values at least one for each vertex. The chromatic number minimum assigned by over colourings G. Introduced Bosica and Tardif, covers are an extension whereby real-valued acts on subgraphs belonging given class graphs. turns out be special instance cover number. In this work we investigate acting (k+1)-clique-free which, although sharing some similarities with k-colourable they exhibit peculiarities. We first show if simple G2 homomorphic image G1, then defined G1 bounded above corresponding G2. make use result obtain bounds associated graphs either n-colourable or : b-colourable.