Large Monochromatic Triple Stars in Edge Colourings | Zendy

Letzter Shoham | Zendy

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Large Monochromatic Triple Stars in Edge Colourings

Author(s) -

Letzter Shoham

Publication year - 2015

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21854

Subject(s) - monochromatic color , combinatorics , mathematics , vertex (graph theory) , graph , triple system , enhanced data rates for gsm evolution , star (game theory) , stars , discrete mathematics , physics , computer science , astrophysics , geometry , optics , artificial intelligence , mathematical analysis

Following problems posed by Gyárfás 2011, we show that for every r ‐edge‐colouring of K n there is a monochromatic triple star of order at least n / ( r − 1 ) , improving Ruszinkó's result 2012. An edge colouring of a graph is called a local r ‐colouring if every vertex spans edges of at most r distinct colours. We prove the existence of a monochromatic triple star with at least r n / ( r 2 − r + 1 ) vertices in every local r ‐colouring of K n .

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