2019/10/11 by Li, Jiaao, Li, Xueliang, Wang, Meiling
#05C05 #05C21 #05C40 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1910.05058
In this paper we study the flow-property of graphs containing a spanning triangle-tree. Our main results provide a structure characterization of graphs with a spanning triangle-tree admitting a nowhere-zero 3-flow. All these graphs without nowhere-zero 3-flows are constructed from K4 by a so-called bull-growing operation. This generalizes a result of Fan et al. in 2008 on triangularly-connected graphs and particularly shows that every 4-edge-connected graph with a spanning triangle-tree has a nowhere-zero 3-flow. A well-known classical theorem of Jaeger in 1979 shows that every graph with two edge-disjoint spanning trees admits a nowhere-zero 4-flow. We prove that every graph with two edge-disjoint spanning triangle-trees has a flow strictly less than 3.