A conjecture of Chung and Graham states that every K 4 ‐free graph on n vertices contains a vertex set of size ? n ∕ 2 ? that spans at most n 2 ∕ 18 edges. We make the first step toward this conjecture by showing that it holds for all regular graphs....
subdivision of K 4 is said to be ISK4-free.For instance, series-parallel graphs and line graph of cubic graphs are ISK4-free (see[6]). A triangle is a graph isomorphic to K 3 .The chromatic number of a graph G, denoted by χ(G), is the smallest integer ksuch that V(G) can ...
摘要:本次讨论班参考的是Wayne Goddard, Honghai Xu老师的《Fractional, Circular, and Defective Coloring of Series-Parallel Graphs》,目标是想推广到Every K5\e -minor-free graph of of girth 2k+2 is fractional (2+1/k)-colorable,但目前仍未实现。编辑...
摘要:本次学习的是Pavol Hell, Xuding Zhu老师的《The Circular chromatic Number of Series-Parallel Graphs》,目标是想推广到Every K4-minor-free graph of girth greater than 2k+1 has hom to H (some series of particular graphs),目前独立已论证 k=2 时成立,但 k>2 时数学归纳法无法成立。或许其他方...
It then follows that for $k \\ge 2$, every $\\frac{1}{k-1}$-tough $K_4$-minor-free graph has a spanning $k$-tree, and hence a spanning $k$-walk. Our main proof uses a technique where we incorporate toughness-related information into weights associated with vertices and cutsets...
Let f 3,4(n), for a natural number n, be the largest integer m such that every K 4-free graph of order n contains an induced triangle-free subgraph of order m. We prove that for every suffciently large n, f 3,4(n)≤n 1/2(lnn)120. By known results, this bound is tight ...
K 4-minor free graph neighbor sum distinguishing (nsd) 05C15 05C78 Authors Hualong Li (1) Bingqiang Liu (1) Guanghui Wang (1) Author Affiliations 1. School of Mathematics, Shandong University, Jinan, 250100, China Continue reading... To view the rest of this content please follow the...
摘要:本篇文章学习的是Min Chen, Andre Raspaud的《Homomorphisms from sparse graphs to the Petersen graph》,目标是学习其中关于图 B 的构建并寻求类似于all k− good property的内蕴性质,原文中的核心定理为For a graph B of odd-girth 2k+1 , the existence of a k-partial distance-graph of B with...
Any 7-Chromatic Graphs HasK7OrK4,4As A Minor In 1943, Hadwiger made the conjecture that every k-chromatic graph has a K (k) -minor. This conjecture is, perhaps, the most interesting conjecture of all ... KI Kawarabayashi,B Toft - 《Combinatorica》 被引量: 65发表: 2005年 ...
We present a necessary and sufficient condition for a graph of odd-girth 2 k + 1 to bound the class of K 4 -minor-free graphs of odd-girth (at least) 2 k + 1 , that is, to admit a homomorphism from any such K 4 -minor-free graph. This yields a polynomial-time algorithm to ...