Spectral Extremal Results with Forbidding Linear Forests

The Turán type extremal problems ask to maximize the number of edges over all graphs which do not contain fixed subgraphs. Similarly, their spectral counterparts ask to maximize spectral radius of all graphs which do not contain fixed subgraphs. In this paper, we determine the maximum spectral radiu...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 35; no. 1; pp. 335 - 351
Main Authors: Chen, Ming-Zhu, Liu, A-Ming, Zhang, Xiao-Dong
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.01.2019
Springer Nature B.V
Subjects:
Combinatorics
Engineering Design
Forests
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Original Paper
Spectra
Linear forest
05C50
Spectral radius
Turán type extremal problem
Bipartite graph
05C35
Spectral counterparts
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary:The Turán type extremal problems ask to maximize the number of edges over all graphs which do not contain fixed subgraphs. Similarly, their spectral counterparts ask to maximize spectral radius of all graphs which do not contain fixed subgraphs. In this paper, we determine the maximum spectral radius of all graphs without a linear forest as a subgraph and all the extremal graphs. In addition, the maximum number of edges and spectral radius of all bipartite graphs without k · P 3 as a subgraph are obtained and all the extremal graphs are also determined. Moreover, some relations between Turán type extremal problems and their spectral counterparts are discussed.
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-018-1996-3