Upper bounds of proper connection number of graphs

Fei Huang (), Xueliang Li () and Shujing Wang ()
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Fei Huang: Nankai University
Xueliang Li: Nankai University
Shujing Wang: Nankai University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 1, No 10, 165-173

Abstract: Abstract A path in an edge-colored graph is called a proper path if no two adjacent edges of the path are colored with one same color. An edge-colored graph is proper connected if any two distinct vertices of the graph are connected by a proper path in the graph. For connected graph G, the smallest number of colors that are needed in order to make G proper connected is called the proper connection number of G, denoted by pc(G). In this paper, we present an upper bound for the proper connection number of a graph in terms of the bridge-block tree of the graph. We also use this upper bound as an efficient tool to investigate the Erdös-Gallai-type problem for the proper connection number of a graph.

Keywords: Proper connection number; Bridge-block tree; Erdös-Gallai-type problem; 05C15; 05C35; 05C38; 05C40 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0056-2

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