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Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kierstead, H.A., Trotter, W.T.
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Graphs containing finite induced paths of unbounded length [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The age $\mathcal{A}(G)$ of a graph $G$ (undirected and without loops) is the collection of finite induced subgraphs of $G$, considered up to isomorphy and ordered by embeddability. It is well-quasi-ordered (wqo) for this order if it contains no infinite
Maurice Pouzet, Imed Zaguia
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On Triangle‐Free Graphs That Do Not Contain a Subdivision of the Complete Graph on Four Vertices as an Induced Subgraph [PDF]
Journal of Graph Theory, 2014 We prove a decomposition theorem for the class of triangle‐free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least five in this class is 3‐colorable.
Nicolas Trotignon, Kristina Vuskovic
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Reconfiguration of Regular Induced Subgraphs
, 2022 We study the problem of checking the existence of a step-by-step transformation of $d$-regular induced subgraphs in a graph, where $d \ge 0$ and each step in the transformation must follow a fixed reconfiguration rule. Our problem for $d=0$ is equivalent to \textsc{Independent Set Reconfiguration}, which is one of the most well-studied reconfiguration ...
Hiroshi Eto +4 more
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Electronic Notes in Discrete Mathematics, 2017 In descending generality I survey: five partial orderings of graphs, the induced-subgraph ordering, and examples like perfect, threshold, and mock threshold graphs. The emphasis is on how the induced subgraph ordering differs from other popular orderings and leads to different basic questions.
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The line completion number of hypercubes
AKCE International Journal of Graphs and Combinatorics, 2019 In 1992, Bagga, Beineke, and Varma introduced the concept of the super line graph of index of a graph denoted by The vertices of are the -subsets of and two vertices and are adjacent if there exist and such that and are adjacent edges in They also ...
S.A. Tapadia, B.N. Waphare
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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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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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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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Induced Subgraphs and Path Decompositions
The Electronic Journal of Combinatorics, 2023 A graph $H$ is an induced subgraph of a graph $G$ if a graph isomorphic to $H$ can be obtained from $G$ by deleting vertices. Recently, there has been significant interest in understanding the unavoidable induced subgraphs for graphs of large treewidth.
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