Jianguo Qian

activity

20172022

most citedOn non-empty cross-intersecting families

1 citations · 1 across the 18 of their papers we have counts for

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18 papers · 1 filter

math.CO2022

Graphs with second largest eigenvalue less than $1/2$

Xiaoxia Wu, Jianguo Qian, Haigen Peng

We characterize the simple connected graphs with the second largest eigenvalue less than 1/2, which consists of 13 classes of specific graphs. These 13 classes hint that $c_{2}\in…

math.CO2022

The list-coloring function of signed graphs

Sumin Huang, Jianguo Qian, Wei Wang

It is known that, for any $k$ -list assignment $L$ of a graph $G$ , the number of $L$ -list colorings of $G$ is at least the number of the proper $k$ -colorings of $G$ when $k>(m-1)/\l…

math.CO2022

Menger-type connectivity of line graphs of faulty hypercubes

Huanshen Jia, Jianguo Qian

A connected graph $G$ is called strongly Menger edge connected if $G$ has min\{deg $_{G} (x)$ , deg $_{G} (y)$ \} edge-disjoint paths between any two distinct vertices $x$ and $y$ in $G$ . In…

math.CO2021

The maximum number of stars in a graph without linear forest

Sumin Huang, Jianguo Qian

For two graphs $J$ and $H$ , the generalized Turán number, denoted by $e x (n, J, H)$ , is the maximum number of copies of $J$ in an $H$ -free graph of order $n$ . A linear forest $F$ is t…

math.CO2021

Ramsey numbers for complete graphs versus generalized fans

Maoqun Wang, Jianguo Qian

For two graphs $G$ and $H$ , let $r (G, H)$ and $r_{*} (G, H)$ denote the Ramsey number and star-critical Ramsey number of $G$ versus $H$ , respectively. In 1996, Li and Rousseau proved th…

math.CO2021

Extremal Polygonal Cacti for General Sombor Index

Jiachang Ye, Jianguo Qian

The Sombor index of a graph $G$ was recently introduced by Gutman from the geometric point of view, defined as $S O (G) = \sum_{uv \in E (G)} d (u)^{2} + d (v)^{2}$ , where $d (u)$ is the de…

math.CO2021

Hamiltonian cycles in 4-connected planar and projective planar triangulations with few 4-separators

On-Hei Solomon Lo, Jianguo Qian

Whitney proved in 1931 that every 4-connected planar triangulation is hamiltonian. Later in 1979, Hakimi, Schmeichel and Thomassen conjectured that every such triangulation on $n$ …

math.CO2020

Flips on homologous orientations of surface graphs with prescribed forbidden facial circuits

Weijuan Zhang, Jianguo Qian

Let $G$ be a graph embedded on an orientable surface. Given a class $C$ of facial circuits of $G$ as a forbidden class, we give a sufficient-necessary condition for that an…

math.CO2020★ 1 cited

On non-empty cross-intersecting families

Chao Shi, Peter Frankl, Jianguo Qian

Let $2^{[n]}$ and $(i [ n ])$ be the power set and the class of all $i$ -subsets of ${1, 2, \dots, n}$ , respectively. We call two families $A$ and $B$ cross…

math.CO2019

Generalized spectral characterization of mixed graphs

Wei Wang, Lihong Qiu, Jianguo Qian

A mixed graph $G$ is a graph obtained from a simple undirected graph by orientating a subset of edges. $G$ is self-converse if it is isomorphic to the graph obtained from $G$ by re…

math.CO2019

An Ore-type condition for existence of two disjoint cycles

Maoqun Wang, Jianguo Qian

Let $n_{1}$ and $n_{2}$ be two integers with $n_{1}, n_{2} \geq 3$ and $G$ a graph of order $n = n_{1} + n_{2}$ . As a generalization of Ore's degree condition for the existence of Hamilto…

math.CO2018

A generalization of Noel-Reed-Wu Theorem to signed graphs

Wei Wang, Jianguo Qian

Let $Σ$ be a signed graph where two edges joining the same pair of vertices with opposite signs are allowed. The zero-free chromatic number $χ^{*} (Σ)$ of $Σ$ is the minimum even inte…

math.CO2018

Alon-Tarsi number of signed planar graphs

Wei Wang, Jianguo Qian

Let $(G, σ)$ be any signed planar graph. We show that the Alon-Tarsi number of $(G, σ)$ is at most 5, generalizing a recent result of Zhu for unsigned case. In addition, if $(G, σ)$ i…

math.CO2018

Chromatic-choosability of hypergraphs with high chromatic number

Wei Wang, Jianguo Qian

It was conjectured by Ohba and confirmed recently by Noel et al. that, for any graph $G$ , if $∣ V (G) ∣ \leq 2 χ (G) + 1$ then $χ_{l} (G) = χ (G)$ . This indicates that the graphs with high chroma…

math.CO2018

Flow polynomials of a signed graph

Jianguo Qian

In contrast to ordinary graphs, the number of the nowhere-zero group-flows in a signed graph may vary with different groups, even if the groups have the same order. In fact, for a…

math.CO2018

Colorings v.s. list colorings of uniform hypergraphs

Wei Wang, Jianguo Qian, Zhidan Yan

Let $r$ be an integer with $r \geq 2$ and $G$ be a connected $r$ -uniform hypergraph with $m$ edges. By refining the broken cycle theorem for hypergraphs, we show that if $k>\frac{m-1…

math.CO2018

Inclusion-exclusion by ordering-free cancellation

Yin Chen, Jianguo Qian

Whitney's broken circuit theorem gives a graphical example to reduce the number of the terms in the sum of the inclusion-exclusion formula by a predicted cancellation. So far, the…

math.CO2017

Flip-distance between α-orientations of graphs embedded on plane and sphere

Weijuan Zhang, Jianguo Qian, Fuji Zhang

Felsner introduced a cycle reversal, namely the `flip' reversal, for α-orientations (i.e., each vertex admits a prescribed out-degree) of a graph G embedded on the plane and furthe…

Graphs with second largest eigenvalue less than 1/2

The list-coloring function of signed graphs

Menger-type connectivity of line graphs of faulty hypercubes

The maximum number of stars in a graph without linear forest

Ramsey numbers for complete graphs versus generalized fans

Extremal Polygonal Cacti for General Sombor Index

Hamiltonian cycles in 4-connected planar and projective planar triangulations with few 4-separators

Flips on homologous orientations of surface graphs with prescribed forbidden facial circuits

On non-empty cross-intersecting families

Generalized spectral characterization of mixed graphs

An Ore-type condition for existence of two disjoint cycles

A generalization of Noel-Reed-Wu Theorem to signed graphs

Alon-Tarsi number of signed planar graphs

Chromatic-choosability of hypergraphs with high chromatic number

Flow polynomials of a signed graph

Colorings v.s. list colorings of uniform hypergraphs

Inclusion-exclusion by ordering-free cancellation

Flip-distance between α-orientations of graphs embedded on plane and sphere

Graphs with second largest eigenvalue less than $1/2$