The principal Erd\H{o}s--Gallai differences of a degree sequence

Autor:	Barrus, Michael D.
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics 05C07 (Primary) 05C50 05C75 (Secondary)
Druh dokumentu:	Working Paper
Popis:	The Erd\H{o}s--Gallai criteria for recognizing degree sequences of simple graphs involve a system of inequalities. Given a fixed degree sequence, we consider the list of differences of the two sides of these inequalities. These differences have appeared in varying contexts, including characterizations of the split and threshold graphs, and we survey their uses here. Then, enlarging upon properties of these graph families, we show that both the last term and the maximum term of the principal Erd\H{o}s--Gallai differences of a degree sequence are preserved under graph complementation and are monotonic under the majorization order and Rao's order on degree sequences. Comment: 21 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2107.07643 Zobrazit plný text záznamu View this record from Arxiv