Results 81 to 90 of about 96,090 (258)
Journal of Graph Theory, EarlyView.ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
wiley +1 more source
Note on group distance magic complete bipartite graphs [PDF]
, 2013 A Γ-distance magic labeling of a graph G = (V, E) with |V| = n is a bijection ℓ from V to an Abelian group Γ of order n such that the weight $$w(x) = \sum\nolimits_{y \in N_G (x)} {\ell (y)}$$ of every vertex x ∈ V is equal to the same element µ ∈ Γ ...
S. Cichacz
semanticscholar +1 more source
Tree Independence Number III. Thetas, Prisms and Stars
Journal of Graph Theory, EarlyView.ABSTRACT We prove that for every t ∈ N $t\in {\mathbb{N}}$ there exists τ = τ ( t ) ∈ N $\tau =\tau (t)\in {\mathbb{N}}$ such that every (theta, prism, K 1 , t ${K}_{1,t}$)‐free graph has tree independence number at most τ $\tau $ (where we allow “prisms” to have one path of length zero).
Maria Chudnovsky +2 more
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On Odd Covers of Cliques and Disjoint Unions
Journal of Graph Theory, EarlyView.ABSTRACT Babai and Frankl posed the “odd cover problem” of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order n $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always ⌈ n / 2 ⌉ $\lceil n/2\rceil $ or ⌈ n /
Calum Buchanan +7 more
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Explicit 3‐colorings for Exponential Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento +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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Effects on Seidel energy of two special types of graphs by perturbing edges
Kuwait Journal of ScienceLet G be a simple undirected graph, and let S(G) be its Seidel matrix. The Seidel energy of G is defined as ES(G)=∑i=1n|λS(G)|, where λS(G),λS(G),…,λS(G) are Seidel eigenvalues of G.
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Star-path and star-stripe bipartite Ramsey numbers in multicoloring [PDF]
Transactions on Combinatorics, 2015 For given bipartite graphs G 1 ,G 2 ,…,G t , the bipartite Ramsey number bR(G 1 ,G 2 ,…,G t ) is the smallest integer n such that if the edges of the complete bipartite graph K n,n are partitioned into t disjoint color classes giving t ...
Ghaffar Raeisi
doaj
Soil Contamination Around the Copper Smelter and the Use of Soil Microarthropods as Bioindicators
Land Degradation &Development, EarlyView.ABSTRACT Soil contamination from smelter emissions, including heavy metals (HM), rare earth elements (REEs), and sulfur, poses a significant threat to soil ecosystems. In the immediate vicinity of the Głogów Copper Smelter, HM concentrations were several times higher than in more distant forest stands.
Jacek Malica +10 more
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The Bipartite-Splittance of a Bipartite Graph
Discussiones Mathematicae Graph Theory, 2019 A bipartite-split graph is a bipartite graph whose vertex set can be partitioned into a complete bipartite set and an independent set. The bipartite- splittance of an arbitrary bipartite graph is the minimum number of edges to be added or removed in ...
Yin Jian-Hua, Guan Jing-Xin
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