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1. Jan. 2024 · Improved bounds on the edge-fault diameter were given for triangle-free graphs, but not for C 4-free graphs. The aim of this paper is to fill this gap by presenting best possible bounds on the k-edge-fault diameter for C 4-free graphs.
4. Apr. 2012 · This note focuses on a wider class of edge ideals: the C 4-free edge ideals. As we will see, such ideals arise naturally when we study edge ideals whose powers have linear minimal free resolutions. We say that I G is C 4 -free if the complement graph G c has no induced 4-cycles.
- Eran Nevo, Irena Peeva
- 2013
25. Dez. 2023 · A path decomposition of a graph $G$ is a pair $ (P,X)$ where $P$ is a path with vertex set $\ {1, \ldots, q\}$, and $X = \ {X_1,X_2, \ldots ,X_q\}$ is a family of vertex subsets of $V (G)$ such that: $\bigcup_ {p \in \ {1,\ldots ,q\}} X_p = V (G)$. $\forall\ {u,v\} \in E (G) \exists p \colon u, v \in X_p$.
1. Mai 2013 · This graph is C 4 -free, has q 2 vertices degree q+ 1, and q+1ofdegreeq, for a total of 1 2 q(q+ 1) 2 edges. Füredi determined the first exact result that encompasses infinitely many n, namely that ex(q 2 + +1,C 4 ) 1 2 q(q+1) 2 for q> 13 [7,8], with equality if and only if the graph is an orthogonal polarity aph of a plane of ...
- Frank A. Firke, Peter M. Kosek, Evan D. Nash, Jason Williford
- 2013
21. Sept. 2015 · Abstract. We study the topic of “extremal” planar graphs, defining to be the maximum number of edges possible in a planar graph on n vertices that does not contain a given graph H as a subgraph.
5. Sept. 2011 · We show that, with probability tending to 1 as n → ∞, the final graph produced by this process has maximum degree O ( ( n log n) 1/3) and consequently size O ( n4/3 (log n) 1/3 ), which are sharp up to constants. This confirms conjectures of Bohman and Keevash and of Osthus and Taraz, and improves upon previous bounds due to ...
