7 papers
Signed list edge coloring in graphs of bounded treewidth
Li Zhang, You Lu, Zhengke Miao +1
Vizing conjectured that the list edge chromatic number of any graph with maximum degree is at most . This conjecture has been confirmed for several important classes of g…
Signed circuit -covers of signed -minor-free graphs
You Lu, Rong Luo, Zhengke Miao +1
Bermond, Jackson and Jaeger [{\em J. Combin. Theory Ser. B} 35 (1983): 297-308] proved that every bridgeless ordinary graph has a circuit -cover and Fan [{\em J. Combin. The…
The average degree of edge chromatic critical graphs with maximum degree seven
Yan Cao, Rong Luo, Zhengke Miao +1
In this paper, by developing several new adjacency lemmas about a path on or vertices, we show that the average degree of 7-critical graphs is at least 6. It implies Vizing…
On the size of special class 1 graphs and -co-critical graphs
Gang Chen, Zhengke Miao, Zi-Xia Song +1
A well-known theorem of Vizing states that if is a simple graph with maximum degree , then the chromatic index of is or . A graph is class 1 if $χ'(…
List star edge coloring of generalized Halin graphs
Zhengke Miao, Yimin Song, Tao Wang +1
A star -edge coloring is a proper edge coloring such that there are no bichromatic paths or cycles of length four. The smallest integer such that admits a star -edge…
On the local base set of primitive and nonpowerful signed digraphs
Guanglong Yu, Zhengke Miao
In this paper, we consider the local bases of primitive nonpowerful sign pattern matrices, show that there are "gaps" in the local base set and characterize some sign pattern matri…
Identifying codes and locating-dominating sets on paths and cycles
Chunxia Chen, Changhong Lu, Zhengke Miao
Let be a graph and let be an integer. For a set , define and , where denot…