It is shown that, if t is an integer !3 and not equal to 7 or 8, then there is a unique maximal graph having the path P t as a star complement for the eigenvalue Γ2: The maximal graph is the line graph of K m,m if t ΒΌ 2mΓ1, and of K m,m ΓΎ1 if t ΒΌ 2m. This result yields a characterization of L(G ) wh
Paths in bipartite graphs with color-inverting involutions
β Scribed by Gert Sabidussi
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 681 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
We consider connected bipartite graphs that have a color-inverting involution and do not contain an induced path of length 5. It is shown that such graphs have a color-preserving involution or a dominating edge, or else contain one of two simple forbidden subgraphs.
π SIMILAR VOLUMES
In this paper we obtain two sufficient conditions, Ore type (Theorem 1) and Dirac type (Theorem 2). on the degrees of a bipartite oriented graph for ensuring the existence of long paths and cycles. These conditions are shown to be the best possible in a sense. An oriented graph is a digraph without
## Abstract We give necessary and sufficient conditions for the existence of an alternating Hamiltonian cycle in a complete bipartite graph whose edge set is colored with two colors.
## Abstract Sufficient degree conditions for the existence of properly edgeβcolored cycles and paths in edgeβcolored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edgeβcolored multigraph of order __n__ on at least three colors and with minimum colored degre