Results 51 to 60 of about 69,865 (208)
Rainbow connection and forbidden subgraphs
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Premysl Holub +3 more
openaire +1 more source
Line Graphs of Multigraphs and the Forbidden Graph E 6
Journal of Graph Theory, EarlyView.ABSTRACT The line graph Γ of a multigraph Δ is the graph whose vertices are the edges of Δ, where two such edges are adjacent if and only if they meet in a single vertex of Δ. We provide several characterizations of such line graphs and in particular show that a graph is a line graph if and only if it does not contain one of the 32 graphs, all of which
Hans Cuypers
wiley +1 more source
Characterizing the forbidden pairs for graphs to be super-edge-connected
AKCE International Journal of Graphs and CombinatoricsLet [Formula: see text] be a set of given connected graphs. A graph G is said to be [Formula: see text]-free if G contains no H as an induced subgraph for any [Formula: see text].
Hazhe Ye, Yingzhi Tian
doaj +1 more source
A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2
Algorithms, 2021 Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of
Serafino Cicerone
doaj +1 more source
On Sparsity Conditions Guaranteeing a Fractional Coloring
Journal of Graph Theory, EarlyView.ABSTRACT A graph has an ( a : b ) $(a:b)$ ‐coloring if there exists an assignment from the vertices to subsets of { 1 , … , a } $\{1,\ldots ,a\}$ with size b $b$ such that adjacent vertices are assigned disjoint subsets. Odd girth at least 2 k + 1 $2k+1$ is a necessary condition for a graph to have a ( 2 k + 1 : k ) $(2k+1:k)$‐coloring.
Ilkyoo Choi
wiley +1 more source
Subgraph isomorphism on graph classes that exclude a substructure [PDF]
, 2019 We study Subgraph Isomorphism on graph classes defined by a fixed forbidden graph. Although there are several ways for forbidding a graph, we observe that it is reasonable to focus on the minor relation since other well-known relations lead to either ...
van der Zanden, Tom C. +20 more
core +6 more sources
Decomposition of 4k-regular graphs into k 4-regular K5-free and (K5−e)-free subgraphs [PDF]
Discrete Mathematics Letters, 2021 Rachel Johnson +4 more
doaj +1 more source
On the 12-Representability of Induced Subgraphs of a Grid Graph
Discussiones Mathematicae Graph Theory, 2022 The notion of a 12-representable graph was introduced by Jones, Kitaev, Pyatkin and Remmel in [Representing graphs via pattern avoiding words, Electron. J. Combin. 22 (2015) #P2.53].
Chen Joanna N., Kitaev Sergey
doaj +1 more source
Saturated Partial Embeddings of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
wiley +1 more source
Ramsey-type Theorems with Forbidden Subgraphs [PDF]
Combinatorica, 2001 P. Erdős and A. Hajnal conjectured that for every finite graph \(H\) every \(H\)-free graph on \(n\) vertices contains a complete or empty subgraph of size \(n^{\varepsilon(H)}\). It is shown that if the conjecture holds for \(H_1\), \(H_2\) then it holds for the graph which is \(H_1\) with one vertex blown up to a copy of \(H_2\).
Alon, Noga +2 more
openaire +2 more sources