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On the ρ-Edge Stability Number of Graphs
Discussiones Mathematicae Graph Theory, 2022 For an arbitrary invariant ρ(G) of a graph G the ρ-edge stability number esρ(G) is the minimum number of edges of G whose removal results in a graph H ⊆ G with ρ(H) ≠ ρ(G) or with E(H) = ∅.
Kemnitz Arnfried, Marangio Massimiliano
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Properties of Large 2-Crossing-Critical Graphs
Journal of Graph Algorithms and Applications, 2022 A $c$-crossing-critical graph is one that has crossing number at least $c$ but each of its proper subgraphs has crossing number less than $c$. Recently, a set of explicit construction rules was identified by Bokal, Oporowski, Richter, and Salazar to ...
Drago Bokal +6 more
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The chromatic distinguishing index of certain graphs
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing index of a graph , denoted by , is the least number of labels in an edge coloring of not preserved by any non-trivial automorphism. The distinguishing chromatic index of a graph is the least number such that has a proper edge coloring ...
Saeid Alikhani, Samaneh Soltani
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The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards, Keith
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Journal of Graph Theory, 2012 AbstractThe star chromatic index of a graph G is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi‐colored. We obtain a near‐linear upper bound in terms of the maximum degree . Our best lower bound on in terms of Δ is valid for complete graphs. We also consider the special case
Zdenek Dvorák 0001 +2 more
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Discrete Mathematics, 2004 Given positive integers \(k,d,\;k \geq 2d\), a \((k,d)\)-edge coloring of a graph \(G\) is a mapping \(c:\;E(G) \to \{0,1,\dots, k-1\}\) such that \(d \leq | c(e_i) - c(e_j)| \leq k-d\) whenever two edges \(e_i,e_j\) are adjacent. The authors introduce the circular chromatic index \(\chi_c'(G)\) defined as \(\chi_c'(G) = \inf\{\frac{k}{d}:\;G\) has a \(
Andrea Hackmann, Arnfried Kemnitz
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Acyclic chromatic index of chordless graphs
Discrete Mathematics, 2023 An acyclic edge coloring of a graph is a proper edge coloring in which there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $a'(G)$, is the minimum positive integer $k$ such that $G$ has an acyclic edge coloring with $k$ colors.
Manu Basavaraju +2 more
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The fractional chromatic number of triangle-free subcubic graphs [PDF]
, 2014 Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14 / 5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free ...
Král’, Daniel +5 more
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The b-chromatic index of graphs
Discrete Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Campos +10 more
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The chromatic index of strongly regular graphs [PDF]
, 2021 We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree k ≤ 18 and their complements, the Latin square graphs and their complements, and the triangular ...
Guo, K.; id_orcid +6 more
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