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On Traceability of Claw-_(o-1)-heavy Graphs

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 444-451页

作者： Bin-long LI sheng-gui zhang Department of Applied Mathematics and Xi'an-Budapest Joint Research Center for Combinatorics Northwestern Polytechnical University

A graph is called traceable if it contains a Hamilton path, i.e., a path passing through all the vertices. Let G be a graph on n vertices. G is called claw-o-1-heavy if every induced claw(K_(1,3)) of G has a pair of nonadjacent vertices with degree sum at least n-1 in G. In this paper we show that a claw-o-1-heavy graph G is traceable if we impose certain additional conditions on G involving forbidden induced subgraphs.

关键词： traceable graphs claw-o-1-heavy graphs forbidden subgraphs

Neighbor Sum Distinguishing Total Choice Number of Planar Graphs without 6-cycles

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Acta Mathematica Sinica,English Series 2020年第12期36卷 1417-1428页

作者： Dong Han zhang You LU sheng gui zhang School of Mathematics and Statistics and Xi'an-Budapest Joint Research Center for Combinatorics Northwestern Polytechnical UniversityXi'an 710129P.R.China College of Mathematics and Computer Applications Shangluo UniversityShangluo 726000P.R.China

Pilsniak and Wozniak put forward the concept of neighbor sum distinguishing(NSD)total coloring and conjectured that any graph with maximum degreeΔadmits an NSD total(Δ+3)-coloring in *** 2016,Qu et *** that the list version of the conjecture holds for any planar graph withΔ≥*** this paper,we prove that any planar graph withΔ≥7 but without 6-cycles satisfies the list version of the conjecture.

关键词： Planar graphs neighbor sum distinguishing total choice number Combinatorial Nullstellensatz

On Heavy Paths in 2-connected Weighted Graphs

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 789-798页

作者： Bin-long LI sheng-gui zhang Department of Applied Mathematics School of ScienceNorthwestern Polytechnical UniversityXi'an 710072China

A weighted graph is a graph in which every edge is assigned a non-negative real number. In a weighted graph, the weight of a path is the sum of the weights of its edges, and the weighed degree of a vertex is the sum of the weights of the edges incident with it. In this paper we give three weighted degree conditions for the existence of heavy or Hamilton paths with one or two given end-vertices in 2-connected weighted graphs.

关键词： weighted graph heavy path weighed degree

Bipartite Graphs with the Maximum Sum of Squares of Degrees

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 801-806页

作者： sheng-gui zhang Chun-cao ZHOU Department of Applied Mathematics Northwestern Polytechnical University The State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University AVIC Chengdu Aircraft Design and Research Institute

In this paper we determine all the bipartite graphs with the maximum sum of squares of degrees among the ones with a given number of vertices and edges.

关键词： bipartite graphs sum of squares of degrees extremal graphs

Note on Integer 4-flows in Graphs

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Acta Mathematica Sinica,English Series 2022年第9期38卷 1653-1664页

作者： Xiao WANG You LU sheng gui zhang School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710072P.R.China College of Mathematics and Computer Application Shangluo UniversityShangluo 726000P.R.China

Let G be a bridgeless graph and C be a circuit in *** find a shorter circuit cover of G,Fan proposed a conjecture that if G/C admits a nowhere-zero 4-flow,then G admits a 4-flow(D,f)such that E(G)E(C)?supp(f)and|supp(f)∩E(C)|>3/4|E(C)|,and showed that the conjecture holds if|E(C)|≤19[Combinatorica,37,1097–1112(2017)].In this paper,we prove that the conjecture holds if|E(C)|≤27.

关键词： Integer 4-flow modulo 4-flow circuit

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Neighbor Sum Distinguishing Total Choosability of Planar Graphs with Maximum Degree at Least 10

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 211-224页

作者： Dong-han zhang You Lu sheng-gui zhang Li zhang School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an710129China School of Mathematics and Computer Application Shangluo UniversityShangluo726000China

A neighbor sum distinguishing(NSD)total coloringφof G is a proper total coloring of G such thatΣz∈EG(u)U{u}φ(z)≠Σz∈EG(v)U{v}φ(z)for each edge uv∈E(G),where EG(u)is the set of edges incident with a vertex *** 2015,Pilśniak and Wozniak conjectured that every graph with maximum degreeΔhas an NSD total(Δ+3)-***,Yang et *** that the conjecture holds for planar graphs withΔ≥10,and Qu et *** that the list version of the conjecture also holds for planar graphs withΔ≥*** this paper,we improve their results and prove that the list version of the conjecture holds for planar graphs withΔ≥10.

关键词： planar graphs neighbor sum distinguishing total choosibility combinatorial nullstellensatz discharging method

Degree Conditions Restricted to Induced Paths for Hamiltonicity of Claw-heavy Graphs

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Acta Mathematica Sinica,English Series 2017年第2期33卷 301-310页

作者： Bin Long LI Bo NING sheng gui zhang Department of Applied Mathematics Northwestern Polytechnical University Xi'an 710072 P. R. China European Centre of Excellence NTIS 30614 Pilsen Czech Republic Center for Applied Mathematics Tianjin University Tianjin 300072 P. R. China

Broersma and Veldman proved that every 2-connected claw-free and P6-free graph is hamil- tonian. Chen et al. extended this result by proving every 2-connected claw-heavy and P6-free graph is hamiltonian. On the other hand, Li et al. constructed a class of 2-connected graphs which are claw-heavy and P6-o-heavy but not hamiltonian. In this paper, we further give some Ore-type degree conditions restricting to induced copies of P6 of a 2-connected claw-heavy graph that can guarantee the graph to be hamiltonian. This improves some previous related results.

关键词： Hamiltonian graph forbidden subgraph condition degree condition claw-heavy graph,closure theory

Laplacian Perfect State Transfer in Extended Neighborhood Coronas

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Acta Mathematica Sinica,English Series 2021年第12期37卷 1921-1932页

作者： Yi Peng LI Xiao Gang LIU sheng gui zhang School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710072P.R.China Department of Applied Mathematics Xi'an University of Science and TechnologyXi'an 710054P.R.China Xi'an-Budapest Joint Research Center for Combinatorics Northwestern Polytechnical UniversityXi'an 710129P.R.China

In this paper,we give some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state *** also give some conditions for extended neighborhood coronas to be periodic.

关键词： Laplacian perfect state transfer periodic extended neighborhood corona

A Common Generalization to Theorems on Set Systems with L-intersections

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Acta Mathematica Sinica,English Series 2018年第7期34卷 1087-1100页

作者： Jiu Qiang LIU sheng gui zhang Ji Meng XIAO School of Management Engineering Xi'an University of Finance and Economics Xi'an 710100 P. R. China Department of Mathematics Eastern Michigan University Ypsilanti MI 48197 USA Department of Mathematics Northwestern Polytechnical University Xi'an 710072 P. R. China

In this paper, we provide a common generalization to the well-known Erdos-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well- known theorem on set systems with k-wise E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 （2004）]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.

关键词： Alon-Babai-Suzuki Theorem Erdos-Ko-Rado Theorem Frankl-Wilson Theorem Snevily Theorem multilinear polynomials