Results 41 to 50 of about 332 (184)
Heavy subgraph pairs for traceability of block-chains
Discussiones Mathematicae Graph Theory, 2014 A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type ...
Li Binlong +2 more
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On the chromatic number of (P_{5},windmill)-free graphs [PDF]
Opuscula Mathematica, 2017 In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint ...
Ingo Schiermeyer
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On Critical Unicyclic Graphs with Cutwidth Four
AppliedMath, 2022 The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line Pn with n=|V(G)| vertices in such a way that the maximum number of overlapping edges (i.e., the congestion) is minimized.
Zhenkun Zhang, Hongjian Lai
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Rainbow connection and forbidden subgraphs
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Premysl Holub +3 more
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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
On Sequential Heuristic Methods for the Maximum Independent Set Problem
Discussiones Mathematicae Graph Theory, 2017 We consider sequential heuristics methods for the Maximum Independent Set (MIS) problem. Three classical algorithms, VO [11], MIN [12], or MAX [6] , are revisited. We combine Algorithm MIN with the α-redundant vertex technique[3].
Lê Ngoc C. +2 more
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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
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Stability for large forbidden subgraphs [PDF]
Journal of Graph Theory, 2009 AbstractIn this note we strengthen the stability theorem of Erdős and Simonovits. Write Kr(s1, …, sr) for the complete r‐partite graph with classes of sizes s1, …, sr and Tr(n) for the r‐partite Turán graph of order n. Our main result is:For all r≥2 and all sufficiently small c>0, ε>0, every graph G of sufficiently large order n with e(G)>(1−1/
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Equivalent Formulation of Thomassen's Conjecture Using Tutte Paths in Claw‐Free Graphs
Journal of Graph Theory, EarlyView.ABSTRACT We continue studying Thomassen's conjecture (every 4‐connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2‐connected claw‐free graph has a Tutte cycle), and we extend the equivalent formulation as follows: In every connected claw‐free graph, any two vertices are connected
Adam Kabela +2 more
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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
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