The Erdős-Ko-Rado properties of various graphs containing singletons

DOI10.1016/j.disc.2008.07.021zbMath1177.05082OpenAlexW2090351536MaRDI QIDQ1043643

Peter Borg, F. C. Holroyd

Publication date: 9 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: http://oro.open.ac.uk/17514/1/P_Borg_and_F_Holroyd.pdf

zbMATH Keywords

intersecting familyErdős-Ko-Rado theoremindependent set

Mathematics Subject Classification ID

Extremal set theory (05D05) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (22)

The number of s-separated k-sets in various circles ⋮ On intersecting families of independent sets in trees ⋮ Non-trivial intersecting uniform sub-families of hereditary families ⋮ An analogue of the Erdős-Ko-Rado theorem for weak compositions ⋮ Cross-intersecting subfamilies of levels of hereditary families ⋮ On the Holroyd-Talbot conjecture for sparse graphs ⋮ An Erdős-Ko-Rado theorem for permutations with fixed number of cycles ⋮ Cross-intersecting non-empty uniform subfamilies of hereditary families ⋮ Very well-covered graphs with the Erdős-Ko-Rado property ⋮ Erdös-Ko-Rado theorems for a family of trees ⋮ A non-trivial intersection theorem for permutations with fixed number of cycles ⋮ On the star of the family of independent sets in a graph ⋮ Erdős-Ko-Rado theorems for chordal graphs and trees ⋮ Erdős-Ko-Rado theorems for simplicial complexes ⋮ Intersecting families, cross-intersecting families, and a proof of a conjecture of Feghali, Johnson and Thomas ⋮ Restricted intersecting families on simplicial complex ⋮ Erdös-Ko-Rado theorem for ladder graphs ⋮ Stars on trees ⋮ On stars in caterpillars and lobsters ⋮ Strongly intersecting integer partitions ⋮ A Deza-Frankl type theorem for set partitions ⋮ The Hilton-Spencer cycle theorems via Katona's shadow intersection theorem

Cites Work

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• An Erdős-Ko-Rado theorem for the subcubes of a cube
• An Erdős--Ko--Rado theorem for partial permutations
• Erdős-Ko-Rado-type theorems for colored sets
• The Erdős-Ko-Rado properties of set systems defined by double partitions
• On the maximum number of permutations with given maximal or minimal distance
• An Erdős-Ko-Rado theorem for signed sets
• Compression and Erdős-Ko-Rado graphs
• Graphs with the Erdős-Ko-Rado property
• Intersecting systems of signed sets
• Erdös–Ko–Rado Theorem—22 Years Later
• INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
• Extremal t -intersecting sub-families of hereditary families
• A Group-Theoretic Setting for Some Intersecting Sperner Families
• INTERSECTING FAMILIES OF SEPARATED SETS
• SOME INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
• Intersecting families of permutations

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