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Rainbow copies of C4 in edge-colored hypercubes

2016
*
Discrete Applied Mathematics
*

Michelle Delcourt

doi:10.1016/j.dam.2014.10.002
fatcat:jtzwkh2j35es3lwrnh3ezrrq6u
*Rainbow**Copies**of*C 4*in**Edge*-*Colored**Hypercubes*This process gives a map h : V (Q d ) → V (Q k ). ... that the number*of**rainbow**copies**of*C 4 is maximized.A vertex*in*Q d , say v , has d 2 incident*copies**of*C 4 .Assume that Q d is*edge*-*colored*with*colors*Michelle Delcourt*Rainbow**Copies**of*C 4*in*...##
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Page 8947 of Mathematical Reviews Vol. , Issue 2003m
[page]

2003
*
Mathematical Reviews
*

*In*anti-Ramsey, with n fixed, one seeks the minimum k such that every k-

*edge*

*coloring*

*of*K,, contains a

*rainbow*

*copy*

*of*G, where a

*rainbow*

*copy*is one

*in*which each

*edge*receives a different

*color*. ... The authors

*of*the paper consider the function {(G,H) which denotes the minimum 7 such that every

*edge*

*coloring*

*of*K,, contains either a monochromatic

*copy*

*of*G or a

*rainbow*

*copy*

*of*H. ...

##
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Lower bounds for rainbow Turán numbers of paths and other trees
[article]

2019
*
arXiv
*
pre-print

For a fixed graph F, we would like to determine the maximum number

arXiv:1901.03308v1
fatcat:4xsuvf5fb5ccbcdzech2ye7vhq
*of**edges**in*a properly*edge*-*colored*graph on n vertices which does not contain a*rainbow**copy**of*F, that is, a*copy**of*F all*of*whose ...*edges*receive a different*color*. ... (e)*In*a*rainbow**copy**of*CP (t,1,q) , let x, y, z be the vertices*of*the central path. Then the leaf-*edge*incident to y must have*color*c(xz), or else this*color*does not appear*in*the*rainbow**copy*. ...##
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Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

2016
*
Combinatorics, probability & computing
*

Let ℱ be a family

doi:10.1017/s0963548316000328
fatcat:dfa7fq444batte4o73sy2isctm
*of*graphs and let d be large enough. For every d-regular graph G, we study the existence*of*a spanning ℱ-free subgraph*of*G with large minimum degree. ... To prove these results, we study a locally injective analogue*of*the question. ...*In*terms*of**colorings*, it would suffice to prove the existence*of*a spanning subgraph H with relatively large minimum degree and a*coloring*χ such that all*copies**of*F*in*H are*rainbow*. ...##
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Existence of spanning F-free subgraphs with large minimum degree
[article]

2016
*
arXiv
*
pre-print

Let F be a family

arXiv:1404.7764v2
fatcat:dasddzlrd5d3nmekcgbixixo4y
*of*fixed graphs and let d be large enough. For every d-regular graph G, we study the existence*of*a spanning F-free subgraph*of*G with large minimum degree. ... Here we provide asymptotically tight results for many families*of*bipartite graphs such as cycles or complete bipartite graphs. ...*In*terms*of**colorings*, it would suffice to prove the existence*of*a spanning subgraph H with relatively large minimum degree and a*coloring*χ such that all*copies**of*F*in*H are*rainbow*. ...