On the Weisfeiler-Leman dimension of fractional packing

The k -dimensional Weisfeiler-Leman procedure ( - WL ), which colors -tuples of vertices in rounds based on the neighborhood structure graph, has proven to be immensely fruitful algorithmic study Graph Isomorphism. More generally, it is fundamental importance understanding and exploiting symmetries graphs various settings. Two are -equivalent if produces same final coloring both graphs. 1 -equivalence known as fractional isomorphism graphs, relation becomes finer increases. We investigate what extent standard graph parameters preserved by -equivalence, focusing packing numbers. integral numbers typically NP-hard compute, we discuss applicability -invariance for estimating integrality gap LP relaxation provided their counterparts.