Abstract. Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G.
However, it turns out that dense bipartite graphs are the only counterexamples, in the sense that we can improve. Theorem 1.1 if we forbid a fixed complete ...
Mader asked whether every $C_4$-free graph $G$ contains a subdivision of a complete graph whose order is at least linear in the average degree of $G$.
Mader asked whether every $C_4$-free graph $G$ contains a subdivision of a complete graph whose order is at least linear in the average degree of $G$.
May 6, 2014 · This relates to Steinberg's conjecture. It conjectures that a planar graph wiht no C4 and no C5 is 3-colorable.
A graph is called C4-free if it contains no cycle of length four as an induced subgraph. We prove that if a C4-free graph has n vertices and at least c1n2 ...
Missing: Topological | Show results with:Topological
Large topological cliques in graphs without a 4-cycle. 作者: Daniela Kühn,. Deryk Osthus. Large topological cliques in graphs without a 4-cycle 的封面影像.
Jan 18, 2018 · Let G be an n-vertex graph and MG be the adjacency matrix of the graph G. Then the graph G contains no 4-cycles iff the matrix MG contains no ...
Missing: Cliques | Show results with:Cliques
Aug 3, 2023 · The answer is 2 because we can have the vertex 1 and the edge {2,3}. If we had all of K_3, we could only have a single clique.
We show that any n‐vertex extremal graph G without cycles of length at most k has girth exactly k + 1 if k ≥ 6 and n > ( 2 ( k − 2 ) k − 2 + k − 5 ) / ( k − 3 ) ...