6 citations · 17 across the 14 of their papers we have counts for
14 papers
Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948
Cun-Quan Zhang
OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 198…
Decomposition of class II graphs into two class I graphs
Yan Cao, Guangming Jing, Rong Luo +3
Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum -edge-colorable subgraph and a matching.…
Flows of 3-edge-colorable cubic signed graphs
Liangchen Li, Chong Li, Rong Luo +2
Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs. In this paper, we pr…
The Automatic Quasi-clique Merger algorithm (AQCM)
Scott Payne, Edgar Fuller, George Spirou +1
The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published under the name QCM (quasi-clique merger) [Ou2006, Ou2007, Zhao2011, Qi2014]. The AQ…
Edge-cuts Optimized for Average Weight: a new alternative to Ford and Fulkerson
Scott Payne, Edgar Fuller, Cun-Quan Zhang
Let be a directed graph associated with a weight . For an edge-cut of , the average weight of is denoted and defined as $w_{ave}(Q)=\frac{\s…
Wiener index of unicycle graphs with given number of even degree vertices
Peter Luo, Cun-Quan Zhang, Xiao-Dong Zhang
The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitt…
Flows on signed graphs without long barbells
You Lu, Rong Luo, Michael Schubert +2
Many basic properties in Tutte's flow theory for unsigned graphs do not have their counterparts for signed graphs. However, signed graphs without long barbells in many ways behave…
Flows on flow-admissible signed graphs
Matt DeVos, Jiaao Li, You Lu +3
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero -flow. Bouchet himself proved that such signed graphs admit nowhere-zero $21…
Cycle double covers and non-separating cycles
Arthur Hoffmann-Ostenhof, Cun-Quan Zhang, Zhang Zhang
Which -regular subgraph of a cubic graph can be extended to a cycle double cover of ? We provide a condition which ensures that every satisfying this condition is…
Antimagic orientations of even regular graphs
Tong Li, Zi-Xia Song, Guanghui Wang +2
A labeling of a digraph with arcs is a bijection from the set of arcs of to . A labeling of is antimagic if no two vertices in have the same v…
Signed graphs: from modulo flows to integer-valued flows
Jian Cheng, You Lu, Rong Luo +1
Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modul…
Shortest circuit covers of signed graphs
Jian Cheng, You Lu, Rong Luo +1
A shortest circuit cover of a bridgeless graph is a family of circuits that covers every edge of and is of minimum total length. The total length of a shortest c…
Cycle Double Covers and Semi-Kotzig Frame
Dong Ye, Cun-Quan Zhang
Let be a cubic graph admitting a 3-edge-coloring such that the edges colored by 0 and induce a Hamilton circuit of and the edges colo…
Vertex-Coloring 2-Edge-Weighting of Graphs
Hongliang Lu, Qinglin Yu, Cun-Quan Zhang
A -{\it edge-weighting} of a graph is an assignment of an integer weight, , to each edge . An edge weighting naturally induces a vertex colori…