A Characterization for the Existence of Connected $f$-Factors of $\textit{ Large}$ Minimum Degree

Autor:	Narayanaswamy, N S, Rahul, C S
Rok vydání:	2016
Předmět:	Computer Science - Data Structures and Algorithms Computer Science - Computational Complexity Computer Science - Discrete Mathematics
Druh dokumentu:	Working Paper
Popis:	It is well known that when $f(v)$ is a constant for each vertex $v$, the connected $f$-factor problem is NP-Complete. In this note we consider the case when $f(v) \geq \lceil \frac{n}{2.5}\rceil$ for each vertex $v$, where $n$ is the number of vertices. We present a diameter based characterization of graphs having a connected $f$-factor (for such $f$). We show that if a graph $G$ has a connected $f$-factor and an $f$-factor with 2 connected components, then it has a connected $f$-factor of diameter at least 3. This result yields a polynomial time algorithm which first executes the Tutte's $f$-factor algorithm, and if the output has 2 connected components, our algorithm searches for a connected $f$-factor of diameter at least 3. Comment: 10 pages, Presented in 9th International colloquium on graph theory and combinatorics, 2014
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1601.06291 Zobrazit plný text záznamu View this record from Arxiv