A characterization on (g,f)-parity orientations

2024/04/07 by Hongliang Lu, Lu, Hongliang, Xinxin Ma +1
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Graph Labeling and Dimension Problems #Advanced Mathematical Theories

paper · pdf · doi:10.48550/arxiv.2404.04797

Abstract

Let G be a graph and g,f:V(G)→2^N be two set functions such that g(v)≤ f(v) and g(v)≡ f(v)\pmod 2 for every v∈ V(G). An orientation O of G is called a (g,f)-parity orientation if g(v)≤ d⁺_O(v)≤ f(v) and g(v)≡ d⁺_O(v)\pmod 2 for every v∈ V(G). In this paper, we give a Tutte-type characterization for a graph to have a (g,f)-parity orientation.

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