✦ LIBER ✦

On the Set of Cycle Lengths in a Hamiltonian Graph with a Given Maximum Degree

✍ Scribed by Antoni Marczyk

Publisher: Springer Japan
Year: 2004
Tongue: English
Weight: 278 KB
Volume: 20
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s00373-004-0580-1

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Cycle Lengths in Hamiltonian Graphs with

Cycle Lengths in Hamiltonian Graphs with a Pair of Vertices Having Large Degree Sum

✍ Michael Ferrara; Michael S. Jacobson; Angela Harris 📂 Article 📅 2010 🏛 Springer Japan 🌐 English ⚖ 190 KB

On the largest tree of given maximum deg

On the largest tree of given maximum degree in a connected graph

✍ Y. Caro; I. Krasikov; Y. Roditty 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 258 KB 👁 1 views

## Abstract We prove that every connected graph __G__ contains a tree __T__ of maximum degree at most __k__ that either spans __G__ or has order at least __k__δ(__G__) + 1, where δ(__G__) is the minimum degree of __G.__ This generalizes and unifies earlier results of Bermond [1] and Win [7]. We als

The Number of Independent Sets in a Grap

The Number of Independent Sets in a Graph with Small Maximum Degree

✍ David Galvin; Yufei Zhao 📂 Article 📅 2010 🏛 Springer Japan 🌐 English ⚖ 180 KB

On the number of vertices of given degre

On the number of vertices of given degree in a random graph

✍ Zbigniew Palka 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 115 KB 👁 1 views

This note can be treated a s a supplement to a paper written by Bollobas which was devoted to the vertices of a given degree in a random graph. We determine some values of the edge probability p for which the number of vertices of a given degree of a random graph G E ?An, p) asymptotically has a nor

On the Approximation of Finding A(nother

On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

✍ Cristina Bazgan; Miklos Santha; Zsolt Tuza 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 144 KB

It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP-hard in general, and no polynomial-time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the co

On the maximum number of cycles in a pla

On the maximum number of cycles in a planar graph

✍ R. E. L. Aldred; Carsten Thomassen 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 142 KB 👁 2 views

## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__ = __q__ − __p__ = 1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__ − 1^ = __o__(2^__r__ − 1^) cycles. The planar result is best possib