Linear Polynomial-Time Algorithms To Construct 4-Connected 4-Regular Locally Connected Claw-Free Graphs

  • Authors:

  • Mingchu Li;Liming Xiong;Hong Liu

  • Affiliations:

  • College of Science, Chongqing Technology and Business University, Chongqing, P.R. China, School of Software, Dalian University of Technology, Dalian 116620, China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China;School of Software, Dalian University of Technology, Dalian 116620, China

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
  • Year:
  • 2007

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Abstract

A vertex of a graph is locally connected if its neighborhood is connected. A graph G is locally connected if every vertex of G is locally connected. A graph is called claw-free if it does not contain a copy of K 1,3 as an induced subgraph. In this paper, we provide a constructive characterization of 4-connected 4-regular locally connected claw-free graphs. From its proof, we can give a linear polynomial-time algorithm to construct a 4-connected 4-regular locally connected claw-free graph.