TY - JOUR

T1 - Anti-Ramsey Numbers of Graphs with Small Connected Components

AU - Gilboa, Shoni

AU - Roditty, Yehuda

N1 - Publisher Copyright:
© 2015, Springer Japan.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The anti-Ramsey number, AR(n, G), for a graph G and an integer (Formula presented.) , is defined to be the minimal integer r such that in any edge-colouring of (Formula presented.) by at least r colours there is a multicoloured copy of G, namely, a copy of G that each of its edges has a distinct colour. In this paper we determine, for large enough (Formula presented.) and (Formula presented.) for any large enough t and k, and a graph L satisfying some conditions. Consequently, we determine AR(n, G), for large enough n, where G is (Formula presented.) for any (Formula presented.) and (Formula presented.) for any (Formula presented.) for any (Formula presented.) for any (Formula presented.) , and (Formula presented.) for any (Formula presented.). Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is (Formula presented.) and (Formula presented.) for any (Formula presented.).

AB - The anti-Ramsey number, AR(n, G), for a graph G and an integer (Formula presented.) , is defined to be the minimal integer r such that in any edge-colouring of (Formula presented.) by at least r colours there is a multicoloured copy of G, namely, a copy of G that each of its edges has a distinct colour. In this paper we determine, for large enough (Formula presented.) and (Formula presented.) for any large enough t and k, and a graph L satisfying some conditions. Consequently, we determine AR(n, G), for large enough n, where G is (Formula presented.) for any (Formula presented.) and (Formula presented.) for any (Formula presented.) for any (Formula presented.) for any (Formula presented.) , and (Formula presented.) for any (Formula presented.). Furthermore, we obtain upper and lower bounds for AR(n, G), for large enough n, where G is (Formula presented.) and (Formula presented.) for any (Formula presented.).

KW - Anti-Ramsey

KW - Multicoloured

KW - Rainbow

UR - http://www.scopus.com/inward/record.url?scp=84959178942&partnerID=8YFLogxK

U2 - 10.1007/s00373-015-1581-y

DO - 10.1007/s00373-015-1581-y

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AN - SCOPUS:84959178942

SN - 0911-0119

VL - 32

SP - 649

EP - 662

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 2

ER -