Some extremal results on the colorful monochromatic vertex-connectivity of a graph

Qingqiong Cai (), Xueliang Li () and Di Wu ()
Additional contact information
Qingqiong Cai: Nankai University
Xueliang Li: Nankai University
Di Wu: Nankai University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 4, No 16, 1300-1311

Abstract: Abstract A path in a vertex-colored graph is called a vertex-monochromatic path if its internal vertices have the same color. A vertex-coloring of a graph is a monochromatic vertex-connection coloring (MVC-coloring for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph G, the monochromatic vertex-connection number, denoted by mvc(G), is defined to be the maximum number of colors used in an MVC-coloring of G. These concepts of vertex-version are natural generalizations of the colorful monochromatic connectivity of edge-version, introduced by Caro and Yuster (Discrete Math 311:1786–1792, 2011). In this paper, we mainly investigate the Erdős–Gallai-type problems for the monochromatic vertex-connection number mvc(G) and completely determine the exact value. Moreover, the Nordhaus–Gaddum-type inequality for mvc(G) is also given.

Keywords: Vertex-monochromatic path; MVC-coloring; Monochromatic vertex-connection number; Erdős–Gallai-type problem; Nordhaus–Gaddum-type problem; 05C15; 05C35; 05C38; 05C40 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-018-0258-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:35:y:2018:i:4:d:10.1007_s10878-018-0258-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-018-0258-x

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().