منابع مشابه
Independence and the Havel-Hakimi residue
Favaron et al. (1991) have obtained a proof of a conjecture of Fajtlowicz’ computer program Graffiti that for every graph G the number of zeroes left after fully reducing the degree sequence as in the Havel-Hakimi Theorem is at most the independence number of G. In this paper we present a simplified version of the proof of Graffiti’s conjecture, and we find how the residue relates to a natural ...
متن کاملOn Erdős-Gallai and Havel-Hakimi algorithms
Havel in 1955 [28], Erdős and Gallai in 1960 [21], Hakimi in 1962 [26], Ruskey, Cohen, Eades and Scott in 1994 [69], Barnes and Savage in 1997 [6], Kohnert in 2004 [49], Tripathi, Venugopalan and West in 2010 [83] proposed a method to decide, whether a sequence of nonnegative integers can be the degree sequence of a simple graph. The running time of their algorithms is Ω(n) in worst case. In th...
متن کاملOn Erd\H{o}s-Gallai and Havel-Hakimi algorithms
Havel in 1955 [28], Erdős and Gallai in 1960 [21], Hakimi in 1962 [26], Ruskey, Cohen, Eades and Scott in 1994 [69], Barnes and Savage in 1997 [6], Kohnert in 2004 [49], Tripathi, Venugopalan and West in 2010 [83] proposed a method to decide, whether a sequence of nonnegative integers can be the degree sequence of a simple graph. The running time of their algorithms is Ω(n) in worst case. In th...
متن کاملA Simple Havel-Hakimi Type Algorithm to Realize Graphical Degree Sequences of Directed Graphs
One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edge-sets. Finally, it proves a result which is useful to design an MCMC algorithm to find random realizations of...
متن کاملOn the Annihilation Number of a Graph
In this note, we introduce a graph invariant called the annihilation number and show that it is a sharp upper bound on the independence number. While the invariant does not distinguish between different graphs with the same degree sequence – since it is determined solely by the degrees – it still outperforms many well known upper bounds on independence number. The process which leads to the ann...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00479-b