Eigenvalues and parity factors in graphs with given minimum degree

Abstract

© 2022 Elsevier B.V.Let G be a graph and let g,f be nonnegative integer-valued functions defined on V(G) such that g(v)≤f(v) and g(v)≡f(v)(mod2) for all v∈V(G). A (g,f)-parity factor of G is a spanning subgraph H such that for each vertex v∈V(G), g(v)≤dH(v)≤f(v) and f(v)≡dH(v)(mod2). We prove sharp upper bounds for certain eigenvalues in an h-edge-connected graph G with given minimum degree to guarantee the existence of a (g,f)-parity factor.