Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Ruonan Li; Hajo Broersma; Shenggui Zhang

doi:10.1007/s00373-018-1989-2

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Ruonan Li
, Hajo Broersma
, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively.

Original language	English
Pages (from-to)	261-286
Number of pages	26
Journal	Graphs and Combinatorics
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s00373-018-1989-2
State	Published - 2 Jan 2019

Keywords

Complete graph
Edge-colored graph
Multipartite tournament
Properly edge-colored cycle
Properly edge-colored theta graph

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10.1007/s00373-018-1989-2

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abstract = "With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively.",

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AB - With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edge-colored complete graph to contain a small and a large properly edge-colored theta graph, respectively.

KW - Complete graph

KW - Edge-colored graph

KW - Multipartite tournament

KW - Properly edge-colored cycle

KW - Properly edge-colored theta graph

UR - https://www.scopus.com/pages/publications/85057786575

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Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Abstract

Keywords

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