Characterizations for Degree Sequence Pairs Being Realizable by Graphs

Key Points

• This research aims to identify conditions under which pairs of degree sequences can be realized as graphs.
• Analyzed combinatorial properties of degree sequences.
• Explored necessary and sufficient conditions for realizability.
• Applied graph theoretical approaches to derive characterizations.
• Identified multiple criteria that dictate when degree sequence pairs can form realizable graphs.
• Established correlations between sequence properties and graphical structures.
• Provided formal proofs supporting the characterizations derived.