numberPlanargraphsIn this paper, the acyclic chromatic and the circular list chromatic numbers of a simple H-minor free graph G is considered, where H ∈{K5, K3,3}. It is proved that the acyclic chromatic number (resp. the circular list chromatic number) of a simple H-minor free graph...
For the sake of illustration, and in order to convince the reader that the problem is not quite trivial, we give in full the formula for the number of k-colourings of Bn(4):(73−84k+41k2−10k3+k4)n+(k−1)((73−50k+12k2−k3)n+3(21−22k+8k2−k3)n)+k(k−...
independent sets of edges. Therefore 3 multigraph Mk is Mk is k-colorable. obtained We now recursively de ne multigraphs Mk, k 3 and odd. jvvMoa22fnjk=v?3djM3j2CFa,1vaokr;o3kadr.e:?nnd:l1kJdsa:,eot;bd>vsrikeni2gkunl??el3cvges1t5lkdv3leiv?e3ko.w512t,envdivw6M2t:g7k,hie?
It generalizes several hypergraph parameters, including the Lagrangian, the spectral radius, and the number of edges. This paper presents solutions to several extremal problems about the p-spectral radius of k-partite and k-chromatic hypergraphs of order n. Two of the main results are: (I) Let...
1) circular chromatic number 循环色数1. We first proved that the circular chromatic number of Fr,m,n is 2+1/(n-m/2). 本文中,我们研究了一类平面图-“花图”的循环着色问题,证明了由2r+1个长为2n+1的圈构成的“辐路”长度为m的花图Fr,m,n的循环色数是2+1/(n-m/2),并证明了在这类图...
S+K3x DELTA n2, K3 est un coefficient exprim¢e en mu m<2> ; M4=r2<2> DELTA n2+K4 x DELTA n3, K4 est un coefficient exprim¢e en mu m<2>: 63,9.10<-3> mu m<2> ≤ S ≤ 81,7.10<-3> mu m<2> -201.10<-3> mu m<2> ≤ (r2)<2>x DELTA n2 ≤ -121.10<-3> ...
It is known (N.H. Xuong, J. Combin. Theory 26 (1979) 217–225) that the maximum genus of a graph is mainly determined by its Betti deficiency ξ( G). Let G be a k-edge-connected graph ( k3) whose complementary graph has the chromatic number m. In this paper we prove that ...
We also prove that if G is a connected K3,3-minor free graph with girth at least 5, then the group chromatic number is at most 3. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 51–72, 2006Hong-Jian LaiDepartment of MathematicsXiangwen Li...
We also give an infinite family of strongly non-clique-separable graphs that have chromatic factorisations and a certificate of factorisation for these graphs. We show that every H1 (excluding K3) with χ(H1) ≥ 3, even when H1 contains no triangles, is the chromatic factor of some ...
1) circular chromatic number 循环色数1. We first proved that the circular chromatic number of Fr,m,n is 2+1/(n-m/2). 本文中,我们研究了一类平面图-“花图”的循环着色问题,证明了由2r+1个长为2n+1的圈构成的“辐路”长度为m的花图Fr,m,n的循环色数是2+1/(n-m/2),并证明了在这类图...