The optimal drawings of \(K_{5,n}\)

zbMath1298.05086arXiv1210.1988MaRDI QIDQ463036

Carolina Medina, César Hernández-Vélez, Gelasio Salazar

Publication date: 23 October 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.1988

zbMATH Keywords

crossing numbersantipodal verticesoptimal drawingsTurán's brickyard problemZarankiewicz conjecture

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Planar graphs; geometric and topological aspects of graph theory (05C10) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (13)

Cyclic permutations in determining crossing numbers ⋮ DETERMINING CROSSING NUMBERS OF GRAPHS OF ORDER SIX USING CYCLIC PERMUTATIONS ⋮ The crossing numbers of join products of paths with three graphs of order five ⋮ On the crossing numbers of join products of five graphs of order six with the discrete graph ⋮ The crossing numbers of join products of four graphs of order five with paths and cycles ⋮ ON THE CROSSING NUMBER OF THE JOIN OF THE WHEEL ON FIVE VERTICES WITH THE DISCRETE GRAPH ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Determining crossing number of join of the discrete graph with two symmetric graphs of order five ⋮ On the crossing number of join product of the discrete graph with special graphs of order five ⋮ On the crossing numbers of join products of W_{4}+P_{n} and W_{4}+C_{n} ⋮ Determining crossing numbers of the join products of two specific graphs of order six with the discrete graph ⋮ The crossing numbers of join of special disconnected graph on five vertices with discrete graphs

Cites Work

• Unnamed Item
• Reduction of symmetric semidefinite programs using the regular \(\ast\)-representation
• Zarankiewicz's conjecture is finite for each fixed \(m\)
• Improved Lower Bounds for the 2-Page Crossing Numbers of $K_{m,n}$ and $K_n$ via Semidefinite Programming
• Cyclic‐order graphs and Zarankiewicz's crossing‐number conjecture
• Improved Bounds for the Crossing Numbers of Km,n and Kn
• The crossing number of K5,n
• On a problem of P. Turan concerning graphs

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