✦ LIBER ✦

The stability number and connected -factor in graphs

✍ Scribed by Jiansheng Cai; Guizhen Liu; Jianfeng Hou

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 365 KB
Volume: 22
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.11.002

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a graph with vertex set V (G).

In this work we present a sufficient condition for the existence of connected [k, k + 1]factors in graphs. The condition involves the stability number and degree conditions of graph G.

📜 SIMILAR VOLUMES

Cycles in Graphs with Prescribed Stabili

Cycles in Graphs with Prescribed Stability Number and Connectivity

✍ M. Kouider 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 113 KB

Stability number and [a,b]-factors in gr

Stability number and [a,b]-factors in graphs

✍ Mekkia Kouider; Zbigniew Lonc 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 90 KB

## Abstract A spanning subgraph whose vertices have degrees belonging to the interval [__a,b__], where __a__ and __b__ are positive integers, such that __a__ ≤ __b__, is called an [__a,b__]‐factor. In this paper, we prove sufficient conditions for existence of an [__a,b__]‐factor, a connected [__a,

The number of 1-factors in 2k-connected

The number of 1-factors in 2k-connected graphs

✍ Béla Bollobas 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 166 KB

The number of connected sparsely edged g

The number of connected sparsely edged graphs

✍ E. M. Wright 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 472 KB

## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^‐1^) = __n__^n−2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp

The number of maximal independent sets i

The number of maximal independent sets in connected graphs

✍ Zoltán Füredi 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 286 KB 👁 2 views

Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,

The Number of Removable Edges in 3-Conne

The Number of Removable Edges in 3-Connected Graphs

✍ Su Jianji 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 147 KB

An edge of a 3-connected graph G is said to be removable if G&e is a subdivision of a 3-connected graph. Holton et al. (1990) proved that every 3-connected graph of order at least five has at least W(|G| +10)Â6X removable edges. In this paper, we prove that every 3-connected graph of order at least