May 8, 2017 · Intuitively, a graph that has fewer edges can be properly colored by a smaller number of colors. Kostochka and Yancey 5 confirmed this intuition ...
Sep 18, 2014 · We prove that if G is a 4-critical graph of girth at least five then |E(G)|>=(5|V(G)|+2)/3. As a corollary, graphs of girth at least five embeddable in the ...
May 8, 2017 · for every 4-critical graph G with girth at least five. Moreover, it provides a unified and shorter proof of both a result of Thomassen and a ...
In a recent seminal work, Kostochka and Yancey proved that |E(G)|≥(5|V(G)|-2/3 for every 4-critical graph G. In this article, we prove that ...
Oct 2, 2020 · Chun-Hung Liu, Luke Postle: On the Minimum Edge-Density of 4-Critical Graphs of Girth Five. J. Graph Theory 86(4): 387-405 (2017).
We prove that there exists such that if G is a 5-critical graph, then where is the maximum number of vertex-disjoint cliques of size three or four.
Missing: Five. | Show results with:Five.
Jan 26, 2019 · In Section 4, we use the potential function to study the general structural properties of k-critical graphs that are 'close' to violating ...
People also ask
What is the minimum edge covering in graph theory?
What is the girth of Petersen graph?
Kostochka and Yancey proved that every 5-critical graph G satisfies: |E(G)|≥9/4|V(G)|-5/4. A construction of Ore gives an infinite family of graphs meeting ...
Postle, On the Minimum Edge-Density of 4-Critical Graphs of Girth Five, http://arxiv.org/pdf/1409.5295.pdf. [46] O. Ore, The Four Color Problem, Academic ...
We say that G is a k-Ore graph if it can be obtained from copies of Kk and repeated Ore-compositions. Theorem 1.3 If G be a 5-critical, then |E(G)| = 9n−5. 4.