Results 41 to 50 of about 8,313 (308)
Partitioning graphs into induced subgraphs [PDF]
Discrete Applied Mathematics, 2017 14 pages, 4 ...
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A ramsey-type theorem for multiple disjoint copies of induced subgraphs
Discussiones Mathematicae Graph Theory, 2014 Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to ...
Nakamigawa Tomoki
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CONSTRUCTION OF BICYCLIC GRAPH AND ITS APPLICATION IN TRANS JOGJA ROUTES
Barekeng, 2023 A bicyclic graph is a type of graph that consists of exactly two cycles. A cycle is a graph that is a closed path where no vertices are repeated except the first and last vertices which are the same.
Aditya Ambarwati, Vira Hari Krisnawati
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Induced subgraphs with distinct sizes [PDF]
Random Structures & Algorithms, 2008 AbstractWe show that for every 0 < ϵ < 1/2, there is an n0 = n0(ϵ) such that if n > n0 then every n‐vertex graph G of size at least $\varepsilon \left( {\matrix{ {\matrix{ n \cr 2 \cr } } \cr } } \right)$ and at most $(1- \varepsilon) \left( {\matrix{ {\matrix{ n \cr 2 \cr } } \cr } } \right)$ contains induced k‐vertex subgraphs with at least ...
Noga Alon, Alexandr V. Kostochka
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The complete list of Ramsey $(2K_2,K_4)$-minimal graphs
Electronic Journal of Graph Theory and Applications, 2015 Let $F, G,$ and $H$ be non-empty graphs. The notation $F \rightarrow (G,H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F ...
Kristiana Wijaya +3 more
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Application of an Extremal Result of Erdős and Gallai to the (n,k,t) Problem
Theory and Applications of Graphs, 2017 An extremal result about vertex covers, attributed by Hajnal to Erdős and Gallai, is applied to prove the following: If n, k, and t are integers satisfying n ≥ k ≥ t ≥ 3 and k ≤ 2t - 2, and G is a graph with the minimum number of edges among graphs on n ...
Matt Noble +3 more
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3-degenerate induced subgraph of a planar graph
, 2021 A graph $G$ is $d$-degenerate if every non-null subgraph of $G$ has a vertex of degree at most $d$. We prove that every $n$-vertex planar graph has a $3$-degenerate induced subgraph of order at least $3n/4$.Comment: 28 pages, 12 ...
Oum, Sang-il +12 more
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Efficient Enumeration of Subgraphs and Induced Subgraphs with Bounded Girth [PDF]
, 2018 The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and recent literature. In this paper, we consider the problem of listing connected subgraphs with bounded girth. As a large
Kazuhiro Kurita +4 more
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Edge erasures and chordal graphs
Electronic Journal of Graph Theory and Applications, 2021 We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph.
Jared Culbertson +2 more
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Graphs with distinguishing sets of size k
Kuwait Journal of ScienceThe size of a resolving set R of a non-trivial connected graph Γ of order n ≥ 2 is the number of edges in the induced subgraph .The minimum cardinality of a resolving set of size k of graph Γ is called the metric dimension of size k, denoted by β(k)(Γ ...
Muhammad Naeem Azhar +3 more
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