Results 11 to 20 of about 10,864 (212)
Splits with forbidden subgraphs [PDF]
Discrete Mathematics, 2022 In this note, we fix a graph $H$ and ask into how many vertices can each vertex of a clique of size $n$ can be "split" such that the resulting graph is $H$-free. Formally: A graph is an $(n,k)$-graph if its vertex sets is a pairwise disjoint union of $n$ parts of size at most $k$ each such that there is an edge between any two distinct parts. Let $$ f(
Maria Axenovich, Ryan R. Martin
openaire +4 more sources
Line Graphs and Forbidden Induced Subgraphs
Journal of Combinatorial Theory, Series B, 2001 AbstractBeineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, Šoltés gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases.
Hong‐Jian Lai, Ľubomír Šoltés
openalex +3 more sources
Forbidden Subgraphs of Power Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are connected by an edge between if and only if either $u=v^i$ or $v=u^j$ for some $i$, $j$. A number of important graph classes, including perfect graphs, cographs ...
Manna, Pallabi +2 more
openaire +5 more sources
Toughness, Forbidden Subgraphs and Pancyclicity [PDF]
Graphs and Combinatorics, 2021 AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$
Wei Zheng +4 more
openaire +3 more sources
Forbidden Subgraphs for Existences of (Connected) 2-Factors of a Graph
Discussiones Mathematicae Graph Theory, 2023 Clearly, having a 2-factor in a graph is a necessary condition for a graph to be hamiltonian, while having an even factor in graph is a necessary condition for a graph to have a 2-factor.
Yang Xiaojing, Xiong Liming
doaj +1 more source
Tree in forbidden triples generating a finite set of graphs with high connectivity
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph and a set of connected graphs, is said be -free if does not contain any member of as an induced subgraph. For , we let denote the set of all -connected -free graphs.
Yoshimi Egawa, Zhixian Zhao
doaj +1 more source
Clique minors in graphs with a forbidden subgraph [PDF]
Random Structures & Algorithms, 2021 AbstractThe classical Hadwiger conjecture dating back to 1940s states that any graph of chromatic number at least r has the clique of order r as a minor. Hadwiger's conjecture is an example of a well‐studied class of problems asking how large a clique minor one can guarantee in a graph with certain restrictions.
Jacob Fox +3 more
openaire +4 more sources
Discussiones Mathematicae Graph Theory, 2022 A graph is called Hamiltonian extendable if there exists a Hamiltonian path between any two nonadjacent vertices. In this paper, we give an explicit formula of the minimum number of edges for Hamiltonian extendable graphs and we also characterize the ...
Yang Xiaojing, Xiong Liming
doaj +1 more source
Axioms, 2022 Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for any H∈H. In this article, we characterize all connected subgraph pairs {R,S} guranteeing the edge-connectivity of a connected {R,S}-free graph to ...
Junfeng Du, Ziwen Huang, Liming Xiong
doaj +1 more source
Forbidden Subgraphs for Collapsible Graphs and Supereulerian Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we completely characterize the connected forbidden subgraphs and pairs of connected forbidden subgraphs that force a 2-edge-connected (2-connected) graph to be collapsible.
Liu Xia, Xiong Liming
doaj +1 more source