More on the Erdös-Ko-Rado theorem for integer sequences

Gronau, Hans-Dietrich O. F.

doi:10.1016/0097-3165(83)90013-4

Cited by 14 publications

(11 citation statements)

References 6 publications

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“…, c k s s ; p k 0 ), then the following result holds. (Theorem 2 also generalizes earlier results of Berge [2], Bollobás and Leader [3], and others (see [5][6][7][8][9]14]). )…”

Section: Theorem 1 (See Holroyd Spencer and Talbotsupporting

confidence: 73%

A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table

Hilton

Spencer

2009

Journal of Combinatorial Theory, Series A

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Let G be a graph consisting of powers of disjoint cycles and letA be an intersecting family of independent r-sets of vertices.Provided that G satisfies a further condition related to the clique numbers of the powers of the cycles, then |A| will be as large as possible if it consists of all independent r-sets containing one vertex from a specified cycle. Here r can take any value, 1 rThis generalizes a theorem of Talbot dealing with the case when G consists of a cycle of order n raised to the power k. Talbot showed that |A| n−kr−1 r−1 .

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“…, c k s s ; p k 0 ), then the following result holds. (Theorem 2 also generalizes earlier results of Berge [2], Bollobás and Leader [3], and others (see [5][6][7][8][9]14]). )…”

Section: Theorem 1 (See Holroyd Spencer and Talbotsupporting

confidence: 73%

A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table

Hilton

Spencer

2009

Journal of Combinatorial Theory, Series A

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“…This generalises a well-known result that was first stated by Meyer [31] and proved in different ways by Deza and Frankl [10], Bollobás and Leader [4], Engel [11] and Erdős et al [12], and that can be described by saying that the conjecture is true for F = [n] r . Berge [3] and Livingston [30] had proved (i) and (ii) respectively for the special case F = {[n]} (other proofs are found in [18,32]). In [5] the conjecture is also verified for F uniform and EKR; Holroyd and Talbot [20] had essentially proved (i) for such a family F in a graph-theoretical context.…”

Section: Intersecting Families Of Signed Setsmentioning

confidence: 95%

On t-intersecting families of signed sets and permutations

Borg

2009

Discrete Mathematics

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“…There are several other papers in the general area, for example [1][2][3]7,[10][11][12]14,[16][17][18]24,27].…”

Section: Theorem 13 (See Deza and Franklmentioning

confidence: 98%

Multiple cross-intersecting families of signed sets

Borg¹,

Leader²

2010

Journal of Combinatorial Theory, Series A

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A k-signed r-set on [n] = {1, . . . ,n} is an ordered pair (A, f ), where A is an r-subset of [n] and f is a function from A to [k]. Families A 1 , . . . , A p are said to be cross-intersecting if any set in any family A i intersects any set in any other family A j . Hilton proved a sharp bound for the sum of sizes of cross-intersecting families of r-subsets of [n]. Our aim is to generalise Hilton's bound to one for families of k-signed r-sets on [n]. The main tool developed is an extension of Katona's cyclic permutation argument.

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More on the Erdös-Ko-Rado theorem for integer sequences

Cited by 14 publications

References 6 publications

A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table

A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table

On t-intersecting families of signed sets and permutations

Multiple cross-intersecting families of signed sets

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