A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequen...A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequence of distinct triangles T1T2%…Tk in G such that for 1 〈 i 〈 k - 1, IE（Ti）∩E（Ti＋1）1= 1 and E（Ti） n E（Tj）=φ if j 〉 i＋1. Two edges e, e＇∈ E（G） are triangularly connected if there is a triangle-path T1, T2,... , Tk in G such that e ∈ E（T1） and er ∈ E（Tk）. Two edges e, e＇ ∈E（G） are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph G is Z3-connected, unless it has a triangularly connected component which is not Z3-connected but admits a nowhere-zero 3-flow.展开更多
We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by i...We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by indirect tension(IDT)and semi-circular bending(SCB)test.Thereafter,the low-temperature performance evaluation index suitable for CRM was put forward.Then,the triangular coordinate statistical chart was used to analyze the optimal proportion of three grades of aggregate which are 2.36-4.75 mm,0.075-2.36 mm and below 0.075 mm.The results showed that the W_(f) and G_(f) could distinguish the low-temperature performance of CRM with different mixtures and emulsified asphalt dosage.For cold recycled fine aggregate,2.36-4.75 mm,0.075-2.36 mm and less than 0.075 mm account for 20%-25%,74.3%-80%and 5%-8%,respectively.The CRM with lower void fraction,higher W_(f) and G_(f) could be obtained.Based on the reported findings,it was suggested that the sieve passing percentage of 4.75,2.36,and 0.075 mm of CRM is 45%-55%,27%-52%and 1.5%-5%,respectively.展开更多
文摘A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequence of distinct triangles T1T2%…Tk in G such that for 1 〈 i 〈 k - 1, IE（Ti）∩E（Ti＋1）1= 1 and E（Ti） n E（Tj）=φ if j 〉 i＋1. Two edges e, e＇∈ E（G） are triangularly connected if there is a triangle-path T1, T2,... , Tk in G such that e ∈ E（T1） and er ∈ E（Tk）. Two edges e, e＇ ∈E（G） are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph G is Z3-connected, unless it has a triangularly connected component which is not Z3-connected but admits a nowhere-zero 3-flow.
基金Funded by the Key Research and Development Plan of Jiangxi Province (No. 20223BBG74002)the Natural Science Foundation of China (Nos. 51778483, 51978521)the Fundamental Research Funds for the Central Universities (No. DUT24RC (3)100)。
文摘We optimized the gradation of cold recycled mixture(CRM)based on low-temperature performance.Firstly,the low-temperature crack resistance of CRM with different gradation and emulsified asphalt content was studied by indirect tension(IDT)and semi-circular bending(SCB)test.Thereafter,the low-temperature performance evaluation index suitable for CRM was put forward.Then,the triangular coordinate statistical chart was used to analyze the optimal proportion of three grades of aggregate which are 2.36-4.75 mm,0.075-2.36 mm and below 0.075 mm.The results showed that the W_(f) and G_(f) could distinguish the low-temperature performance of CRM with different mixtures and emulsified asphalt dosage.For cold recycled fine aggregate,2.36-4.75 mm,0.075-2.36 mm and less than 0.075 mm account for 20%-25%,74.3%-80%and 5%-8%,respectively.The CRM with lower void fraction,higher W_(f) and G_(f) could be obtained.Based on the reported findings,it was suggested that the sieve passing percentage of 4.75,2.36,and 0.075 mm of CRM is 45%-55%,27%-52%and 1.5%-5%,respectively.
