A star coloring of a graph is a proper coloring such that no path on four vertices is 2-colored. We prove that every planar graph with girth at least 9 can be star colored using 5 colors, and that every planar graph with girth at least 14 can be star colored using 4 colors; the figure 4 is best possible. We give an example of a girth 7 planar graph that requires 5 colors to star color.

In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We also prove a similar result for the oriented chromatic number, from which follows in particular that graphs of large girth excluding a minor have oriented chromatic number at most 5, and for the pth chromatic number χp, from which follows in...

In this paper, we give two constructions of weakly distance-regular digraphs of girth 2, and prove that certain quotient digraph of a commutative weakly distancetransitive digraph of girth 2 is a distance-transitive graph. As an application of the result, we not only give some constructions of weakly distance-regular digraphs which are not weakly distance-transitive, but determine a special cla...

This paper presents a full-scale deep-water steel catenary riser fatigue test system. The proposed system can carry out tests on risers, hoses, and subsea pipelines up to 21 m in length, ranging from 8 24 inches diameter. was realized by mechanical loading with control systems, could axial tension compression, bending moment, torsion, internal pressure simulate all load types risers or pipeline...

An anthropometric and body composition analysis was conducted on 123 competitive young male football players of different age groups (U13; U15; U17 & U19) with at least 4 years training load. 3D measurement were performed by the NX-16 ([TC]2, scanner Cary, North Carolina). Body measured bioelectrical impedance InBody 720 (Biospace Ltd.). Anthropometric characteristics among asymmetries between ...

We consider the problem of construction of graphs with given degree k and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G. Royle, four of the known cages including the Hoffman-Singleton graph, some graphs constructed by...

Erdős proved that there exist graphs of arbitrarily high girth and arbitrarily high chromatic number. We give a different proof (but also using the probabilistic method) that also yields the following result on the typical asymptotic structure of graphs of high girth: for all ` ≥ 3 and k ∈ N there exist constants C1 and C2 so that almost all graphs on n vertices and m edges whose girth is great...

By proposing two questions on total colorings of cubic graphs of large girth, we investigate a possible connection between girth and total chromatic parameters in cubic graphs.

We consider supercritical bond percolation on a family of high-girth d-regular expanders. Alon, Benjamini and Stacey (2004) established that its critical probability for the appearance of a linearsized (“giant”) component is pc = 1/(d − 1). Our main result recovers the sharp asymptotics of the size and degree distribution of the vertices in the giant at any p > pc, as well as that of its 2-core...

An equitable (t, k, d)-tree-coloring of a graph G is a coloring to vertices of G such that the sizes of any two color classes differ by at most one and the subgraph induced by each color class is a forest of maximum degree at most k and diameter at most d. The minimum t such that G has an equitable (t′, k, d)-tree-coloring for every t′ ≥ t is called the strong equitable (k, d)-vertex-arboricity...