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List Edge Coloring of outer-1-planar graphs

Acta Mathematicae Applicatae Sinica 2020年第3期36卷 737-752页

作者： Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi'an 710071China

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most *** is known that the list edge chromatic numberχ′l(G)of any outer-1-planar graph G with maximum degreeΔ(G)≥5 is exactly its maximum *** this paper,we proveχ′l(G)=Δ(G)for outer-1-planar graphs G withΔ(G)=4 and with the crossing distance being at least 3.

关键词： outerplanar graph outer-1-planar graph crossing distance list edge coloring

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Linear Arboricity of outer-1-planar graphs

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Journal of the Operations Research Society of China 2021年第1期9卷 181-193页

作者： Xin Zhang Bi Li School of Mathematics and Statistics Xidian UniversityXi’an 710071China

A graph is outer-1-planar if it can be drawn in the plane so that all vertices are on the outer face and each edge is crossed at most *** et al.(Edge covering pseudo-outerplanar graphs with forests,Discrete Math 312:2788-2799,2012;MR2945171)proved that the linear arboricity of every outer-1-planar graph with maximum degree△is exactly[△/2] provided that△=3or△≥5 and claimed that there are outer-1-planar graphs with maximum degree △=4 and linear arboricity[[(O+1)/2]=*** is shown in this paper that the linear arboricity of every outer-1-planar graph with maximum degree 4 is exactly 2 provided that it admits an outer-1-planar drawing with crossing distance at least 1 and crossing width at least 2,and moreover,none of the above constraints on the crossing distance and Crossing width can be removed..Besides,a polynomial-time algorithm for constructing a path-2-coloring(i.e.,an edge 2-coloring such that each color class induces a linear forest,a disjoint union of paths)of such an outer-1-planar drawing is given.

关键词： outer-1-planar graph Crossing Linear arboricity Polynomial-time algorithm

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Conflict-free Incidence Coloring of outer-1-planar graphs

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Acta Mathematicae Applicatae Sinica 2024年第4期40卷 929-942页

作者： Meng-ke QI Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi’an 710071China

An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get distinct colors if and only if they conflict each other,i.e.,(i)u=v,(ii)uv is e or f,or(iii)there is a vertex w such that uw=e and vw=*** minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number.A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most *** this paper,we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices,and moreover,all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely *** efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.

关键词： outer-1-planar graph incidence coloring combinatorial algorithm channel assignment problem

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Strong Edge Coloring of outerplane graphs with Independent Crossings

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 467-477页

作者： Ke-Jie LI Xin ZHANG School of Mathematics and Statistics Xidian UniversityXi’an 710071China

The strong chromatic index of a graph is the minimum number of colors needed in a proper edge coloring so that no edge is adjacent to two edges of the same *** outerplane graph with independent crossings is a graph embedded in the plane in such a way that all vertices are on the outer face and two pairs of crossing edges share no common end *** is proved that every outerplane graph with independent crossings and maximum degreeΔhas strong chromatic index at most 4Δ-6 if Δ≥4,and at most 8 ifΔ≤*** bounds are sharp.

关键词： outer-1-planar graph IC-planar graph strong edge coloring crossing

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