Results 51 to 60 of about 63,637 (247)
A note on the generator subgraph of a graph
Electronic Journal of Graph Theory and Applications, 2020 Graphs considered in this paper are finite simple undirected graphs. Let G = (V(G), E(G)) be a graph with E(G) = {e1, e2,..., em}, for some positive integer m. The edge space of G, denoted by ℰ(G), is a vector space over the field ℤ2. The elements of ℰ(
Neil Mores Mame +1 more
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Finding a maximum induced degenerate subgraph faster than 2^n
, 2012 In this paper we study the problem of finding a maximum induced d-degenerate subgraph in a given n-vertex graph from the point of view of exact algorithms. We show that for any fixed d one can find a maximum induced d-degenerate subgraph in randomized (2-
Pilipczuk, Marcin, Pilipczuk, Michał
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Induced subgraphs of hypercubes
European Journal of Combinatorics, 2013 Let $Q_k$ denote the $k$-dimensional hypercube on $2^k$ vertices. A vertex in a subgraph of $Q_k$ is {\em full} if its degree is $k$. We apply the Kruskal-Katona Theorem to compute the maximum number of full vertices an induced subgraph on $n\leq 2^k$ vertices of $Q_k$ can have, as a function of $k$ and $n$. This is then used to determine $\min(\max(|V(
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Maximum Induced Subgraph of an Augmented Cube
, 2014 Let maxζG(m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube, possesses some properties superior to those of the hypercube. We study the cases when G is the augmented cube AQn.
Meng-Jou Chien +2 more
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On matroids induced by packing subgraphs
Journal of Combinatorial Theory, Series B, 1988 AbstractThe main result of the paper is a characterization of connected graphs H with the property: For any graph G, the subsets of vertices that can be saturated by packing edges of G and copies of H are independent sets of a matroid.
Martin Loebl, Svatopluk Poljak
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Improvements on Induced Subgraphs of Given Sizes
Communications in Mathematics and Statistics, 2023 Given integers $m$ and $f$, let $S_n(m,f)$ consist of all integers $e$ such that every $n$-vertex graph with $e$ edges contains an $m$-vertex induced subgraph with $f$ edges, and let $ (m,f)=\limsup_{n\rightarrow\infty} |S_n(m,f)|/\binom{n}{2}$.
He, Jialin, Ma, Jie, Zhao, Lilu
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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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Forbidden subgraph pairs for traceability of block-chains
Electronic Journal of Graph Theory and Applications, 2013 A block-chain is a graph whose block graph is a path, i.e. it is either a $P_1$, a $P_2$, or a 2-connected graph, or a graph of connectivity 1 with exactly two end-blocks. A graph is called traceable if it contains a Hamilton path.
Binlong Li +2 more
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On bounding the difference between the maximum degree and the chromatic number by a constant
, 2016 We provide a finite forbidden induced subgraph characterization for the graph class $\varUpsilon_k$, for all $k \in \mathbb{N}_0$, which is defined as follows.
Schaudt, Oliver, Weil, Vera
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Graphs that do not contain a cycle with a node that has at least two neighbors on it [PDF]
, 2012 We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes of graphs ...
Aboulker, Pierre +3 more
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