Results 81 to 90 of about 5,057 (262)
On l-reconstructibility of degree list of graphs [PDF]
AUT Journal of Mathematics and ComputingThe k-deck of a graph is the multiset of its subgraphs induced by k vertices which is denoted by Dk(G). A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices.
Rajab Ali Borzooei, Mehrnoosh Shadravan
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On Weakly Distinguishing Graph Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A univariate graph polynomial P(G;X) is weakly distinguishing if for almost all finite graphs G there is a finite graph H with P(G;X)=P(H;X). We show that the clique polynomial and the independence polynomial are weakly distinguishing.
Johann A. Makowsky, Vsevolod Rakita
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On matroids induced by packing subgraphs
Journal of Combinatorial Theory, Series B, 1988 The class of those connected graphs H is described such that in any graph the vertex set covered by vertex disjoint copies of H and edges form the independent sets of a matroid. The condition is that H is either critical or has a 1-factor, or, finally, it has a degree-one vertex and a vertex c such that for every \(x\neq c\), H-x has a 1-factor.
Martin Loebl, Svatopluk Poljak
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Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
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Graphs in which every c edges that form a tree are chords of a common cycle
AKCE International Journal of Graphs and Combinatorics, 2020 Consider the k-connected graphs G in which every edges that form a particular type of induced subgraph must all be chords of a common cycle of G. Extending a few known partial results with and new results exploit the structure of the specified type of ...
Terry A. McKee
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Halin's Grid Theorem for Digraphs
Journal of Graph Theory, EarlyView.ABSTRACT Halin showed that every thick end of every graph contains an infinite grid. We extend Halin's theorem to digraphs. More precisely, we show that for every infinite family ℛ ${\rm{ {\mathcal R} }}$ of disjoint equivalent out‐rays there is a grid whose vertical rays are contained in ℛ ${\rm{ {\mathcal R} }}$.
Florian Reich
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On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source
On the Seidel Laplacian spectrum of threshold graphs [PDF]
Journal of HyperstructuresA graph which does not contain C4, P4, or 2K2 as its induced subgraphs, is called a threshold graph. In this paper, we consider seidel laplacian matrix of a connected threshold graph and determine the seidel laplacian spectrum. Also, the characterization
Megha P M, Parvathy K S
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Lower Bounds for Maximum Weight Bisections of Weighted Triangle‐Free Subcubic Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge‐weighted triangle‐free subcubic graphs and show that every weighted triangle‐free subcubic graph G = ( V , E , w ) $G=(V,E,w)$ has a bisection with weight at least θ ⋅ w (
Stefanie Gerke +3 more
wiley +1 more source
Properties of induced subgraphs of random graphs with given degree sequences
, 2022 In this thesis we study induced subgraphs of uniformly random graphs with given degree sequences. We study the degree sequence of these subgraphs and use this to study their properties.
ANGUS JOHN SOUTHWELL (13963878)
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