A remark concerning graphical sequences
نویسندگان
چکیده
In “A note on a theorem of Erdös & Gallai” ([6]) one identifies the nonredundant inequalities in a characterization of graphical sequences. We explain how this result may be obtained directly from a simple geometrical observation involving weak majorization. A sequence of positive integers d1, d2, . . . , dp is called graphical if it is the degree sequence of a graph, i.e., there is a graph whose vertices have degrees d1, d2, . . . , dp. Sierksma and Hoogeveen [5] presents several (actually seven) equivalent conditions for an integer sequence to be graphical. For a further discussion of this topic, see Chapter 7 of [3] or Chapter 3 of [4]. One well-known characterization of graphical sequences is the following theorem of Erdös and Gallai [1]. Theorem 1 ([1]) A nonincreasing sequence of positive integers d1, d2, . . . , dp is graphical if and only if ∑p i=1 di is even and
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 304 شماره
صفحات -
تاریخ انتشار 2005