Z3-connectivity with independent number 2
Fan Yang, Xiangwen Li, and Liangchen Li
TL;DR
This paper proves that 3-edge-connected graphs with an independence number of at most 2 can be contracted to specific small graphs or belong to a particular class, revealing structural properties related to Z3-connectivity.
Contribution
It establishes a characterization of 3-edge-connected graphs with independence number at most 2 concerning Z3-contraction, extending understanding of graph contraction properties.
Findings
Graphs can be contracted to K1 or K4 or belong to a specific class.
Characterization of 3-edge-connected graphs with independence number ≤ 2.
Structural insights into Z3-connectivity for these graphs.
Abstract
Let G be a 3-edge-connected graph on n vertices. It is proved in this paper that if the number of independent set no more than 2, then either G can be Z3-contracted to one of graphs {K1;K4} or G is one of the graphs in Fig. 1.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Complexity and Algorithms in Graphs