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Rainbow copies of C4 in edge-colored hypercubes

József Balogh, Michelle Delcourt, Bernard Lidický, Cory Palmer
2016 Discrete Applied Mathematics
Michelle Delcourt 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  ...

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.  ...

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

Daniel Johnston, Puck Rombach
2019 arXiv   pre-print
For a fixed graph F, we would like to determine the maximum number 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.  ...

Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

G. PERARNAU, B. REED
2016 Combinatorics, probability & computing
Let ℱ be a family 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.  ...

Existence of spanning F-free subgraphs with large minimum degree [article]

Guillem Perarnau, Bruce Reed
2016 arXiv   pre-print
Let F be a family 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.  ...