When doing simple C programming, I encountered the same challenge. On your particular Linux system, /usr/include directory contain many , here header files specific to a Linux OS.
find . -name "*.h" | xargs grep PATH_MAX
You should see several headers defining PATH_MAX; unfortunately this value was defined differently in different headers. Here is a listing from my Ubuntu (I also manually removed some false positive hits from the grep program).
./x86_64-linux-gnu/bits/posix1_lim.h:#define _POSIX_PATH_MAX 256
./X11/InitialI.h:#ifndef PATH_MAX
./X11/InitialI.h:#define PATH_MAX 512
./X11/InitialI.h:#ifndef PATH_MAX
./X11/InitialI.h:#define PATH_MAX MAXPATHLEN
./X11/InitialI.h:#define PATH_MAX 1024
./X11/Xos.h:# define PATH_MAX 4096
./X11/Xwindows.h:#if defined(WIN32) && (!defined(PATH_MAX) || PATH_MAX < 1024)
./X11/Xwindows.h:# undef PATH_MAX
./X11/Xwindows.h:# define PATH_MAX 1024
./X11/Xosdefs.h:# ifndef PATH_MAX
./X11/Xosdefs.h:# define PATH_MAX 4096
./X11/Xosdefs.h:# ifndef PATH_MAX
./X11/Xosdefs.h:# define PATH_MAX 1024
./X11/extensions/XKBsrv.h:#define PATH_MAX MAXPATHLEN
./X11/extensions/XKBsrv.h:#define PATH_MAX 1024
./python2.7/osdefs.h:#ifndef PATH_MAX
./python2.7/osdefs.h:#define PATH_MAX MAXPATHLEN
./python2.7/osdefs.h:#if defined(PATH_MAX) && PATH_MAX > 1024
./python2.7/osdefs.h:#define MAXPATHLEN PATH_MAX
./linux/limits.h:#define PATH_MAX 4096 /* # chars in a path name including nul */
./linux/btrfs.h:#define BTRFS_INO_LOOKUP_PATH_MAX 4080
./linux/un.h:#define UNIX_PATH_MAX 108
The header /linux/limits.h had the largest number and should be the most authentic one to include. Alternative strategy is to define your own with a different name, say PATHLEN (4080 is long enough for most practical situations). My main point is to learn to use find to look for answers to your question.