Search

Your search keyword '"Schiermeyer, I."' showing total 35 results
Start Over Author "Schiermeyer, I."
35 results on '"Schiermeyer, I."'

22. On weights of induced paths and cycles in claw‐free and K1,r‐free graphs

Author

Harant, J., Voigt, M., Jendrol, S., Randerath, B., Ryjáček, Z., and Schiermeyer, I.

Abstract

Let Gbe a K1,r‐free graph (r≥ 3) on nvertices. We prove that, for any induced path or induced cycle on kvertices in G(k≥ 2r− 1 or k≥ 2r, respectively), the degree sum of its vertices is at most (2r− 2)(n− α) where α is the independence number of G. As a corollary we obtain an upper bound on the length of a longest induced path and a longest induced cycle in a K1,r‐free graph. Stronger bounds are given in the special case of claw‐free graphs (i.e., r= 3). Sharpness examples are also presented. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 131–143, 2001

Published
2001
Full Text
View/download PDF

35. ON 2-FACTORS WITH A SPECIFIED NUMBER OF COMPONENTS IN LINE GRAPHS.

Author

CHIBA, S., EGAWA, Y., FUJISAWA, J., SAITO, A., SCHIERMEYER, I., TSUGAKI, M., and YAMASHITA, T.

Subjects
*HAMILTONIAN graph theory, *GRAPH theory
Abstract

Kaiser and Vrána [European J. Combin. 33 (2012), 924{947] showed that every 5-connected line graph of minimum degree at least 6 is hamiltonian, which gives a partial solution to Thomassen's Conjecture on hamiltonicity of line graphs [J. Graph Theory 10 (1986), 309{324]. In this paper, we prove that every 5-connected line graph of sufficiently large order compared with a given positive integer k and of minimum degree at least 6 also has a 2-factor with exactly k cycles. In order to show this result, we investigate minimum degree conditions for the existence of such a 2-factor in hamiltonian line graphs. [ABSTRACT FROM AUTHOR]

Published
2019

Catalog

Books, media, physical & digital resources
See catalog results